Silvano Romano - Academia.edu (original) (raw)
Papers by Silvano Romano
The European Physical Journal D, 2004
Models for the mutual potential energy between two molecules proposed in the scientific literatur... more Models for the mutual potential energy between two molecules proposed in the scientific literature often contain a sum of inverse-power interactions involving pairs of sites belonging to the two particles; in turn, these quantities are functions of a few scalar invariants involved in the problem at hand, and one is often interested in directly obtaining an explicit expression of the potential in terms of the latter; the extensively studied two-centre multipole expansion for the mutual electrostatic energy between two charge distributions is a well-known example of this procedure and of its restrictions. We consider here another, less widely known and possibly complementary, approach, proposed byŠebek some years ago [J. Sebek, Czech. J. Phys. B 38, 1185 (1988)]; the resulting formulae show that this procedure can become computationally favourable for sufficiently high molecular symmetry.
Zeitschrift Naturforschung Teil a, 1974
Physical Review E, 2007
Over the last few years, renewed interest has been raised by the simplified general interaction m... more Over the last few years, renewed interest has been raised by the simplified general interaction models proposed by Straley for mesogenic molecules possessing the D 2h symmetry and capable of producing biaxial nematic order. It has already been shown that, in the presence of certain special symmetries, just two out of the four order parameters that are in general necessary, suffice for the description of a biaxial phase. For some other range of parameters, these reducing symmetries do not hold, and, moreover, a mean-field treatment has to be suitably changed into a minimax strategy, still producing a transition to a low-temperature biaxial phase. Upon studying the general parameter range, we identify as a common feature the behavior of a uniaxial order parameter, attaining a local minimum at the biaxial-to-uniaxial transition temperature, and recognizably increasing away from it. This finding is confirmed by a Monte Carlo simulation.
Physica A: Statistical Mechanics and its Applications, 2003
By now, nematogenic lattice models have been extensively studied in the literature dealing with l... more By now, nematogenic lattice models have been extensively studied in the literature dealing with liquid crystals; they usually involve cylindrically symmetric (uniaxial) particles and pairwise additive interaction potentials. On the other hand, quantum mechanical perturbation theory shows that interatomic or intermolecular potentials are only approximately pairwise additive; the pairwise additivity approximation (PAA) of molecular interactions has been extensively and systematically
Physical Review B, 1993
The present paper considers a classical system, consisting of n-component unit vectors (n = 2, 3)... more The present paper considers a classical system, consisting of n-component unit vectors (n = 2, 3), associated with a one-dimensional lattice (uz~k C Z), and interacting via a translationally invariant pair potential of the long-range, antiferromagnetic and anisotropic form W = W~A, +e~j-k~(au~, "uq"+,6 gz u~, quq, q). Here e is a positive quantity setting energy and temperature scales (i.e., T* = ksT/e), a and b are positive numbers, and uq, g denotes the Cartesian components of the unit vectors, Available rigorous results exclude the existence of order at finite temperature in the isotropic case a = b, whereas spin-wave arguments imply its existence in the anisotropic one a)b & 0, for which no such theorems are known; we report here a simulation study of the extremely anisotropic case a = 1, b = 0. Results obtained over a range of sample sizes suggested the existence of antiferromagnetic order in the thermodynamic limit at finite temperature; we have estimated the transition temperatures to be T, * = 0.19 + 0.01 (n = 2) and T; = 0.15 + 0.01 (n = 3).
Physical Review B, 1990
We consider a classical system, consisting of two-component unit vectors I u"j, associated with a... more We consider a classical system, consisting of two-component unit vectors I u"j, associated with a square lattice, and interacting via translationally and rotationally invariant pair potentials of the long-range and ferromagnetic form W= W, &=-e~x,-xk~u, ul"e&0, p&2, where xi, are the coordinates of the lattice sites, Combining available theoretical results, one can conclude that for all p~4 the system disorders at all finite temperatures and exhibits a transition to a lowtemperature phase with infinite susceptibility (Kosterlitz-Thouless-like transition); theoretical bounds on the transition temperature can also be obtained. We report here Monte Carlo simulation results for the potential model defined by p=4 and estimate its transition temperature to be T, *4 =2.23+0. 03, where T*= kz T/c.
International Journal of Modern Physics B, 1998
Director configurations in nematic Liquid Crystals can be determined by minimizing their elastic ... more Director configurations in nematic Liquid Crystals can be determined by minimizing their elastic free-energy density, on the basis of elastic constants and of specific boundary conditions; in some published cases, this has been obtained by numerical procedures where the elastic free-energy density plays the same role as the overall potential energy in a standard Monte Carlo simulation. The "potentials" used in these papers are short-ranged but, in general, not pairwise additive, unless the three elastic constants are set to a common value, thus reducing the potential to the well-known Lebwohl–Lasher lattice model.On the other hand, one can construct, possibly in different ways, a lattice model with pairwise additive interactions, approximately reproducing the elastic free-energy density, where parameters defining the pair potential are expressed as linear combinations of elastic constants; a nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess (...
International Journal of Modern Physics B, 1996
We have considered a classical spin system, consisting of n-component unit vectors (n = 2, 3), as... more We have considered a classical spin system, consisting of n-component unit vectors (n = 2, 3), associated with a semi-infinite lattice in one dimension {uk, k ∈ N+}, and interacting via inhomogeneous pair potentials, in general anisotropic in spin space, and of the long-range ferromagnetic form [Formula: see text] here ∊ is a positive constant setting energy and temperature scales (i.e. T* = k B T/∊), a ≥ 0, b ≥ 0, and the symbols uj, α denote cartesian components of the spins. For some specific values of the two parameters a and b, and on the basis of available theoretical results, one can prove the existence of an ordering transition taking place at finite temperature, and obtain rigorous upper and lower bounds on the transition temperatures. This holds, for example, when n = 2, 3, a > b = 0 (the models studied in our previous paper), as well as for n = 2, a = b > 0 and n = 3, b > a = 0, where a continuous O(2) symmetry of the interaction is involved. We have studied thes...
International Journal of Modern Physics B, 1999
We have considered a classical lattice-gas model, consisting of a two-dimensional lattice Z2, eac... more We have considered a classical lattice-gas model, consisting of a two-dimensional lattice Z2, each site of which hosts at most one two-component unit vector; particles occupying pairs of nearest-neighbouring sites interact via the ferromagnetic potential [Formula: see text] where νj=0,1 denotes occupation numbers, uj are the unit vectors (classical spins) and ∊ is a positive constant setting energy and temperature scales; the total Hamiltonian is given by [Formula: see text] where ∑{j
International Journal of Modern Physics B, 1996
We have considered a classical spin system, consisting of 3-component unit vectors, associated wi... more We have considered a classical spin system, consisting of 3-component unit vectors, associated with a two-dimensional lattice {uk, k ∈ Z2}, and interacting via a translationally and rotationally invariant pair potential, of the long-range ferromagnetic form [Formula: see text] Here ∊ is a positive constant setting energy and temperature scales (i.e. T* = k B T/∊), and xj denotes dimensionless coordinates of the lattice sites. This potential model is known rigorously to possess an ordering transition at finite temperature, and has been characterized quantitatively by Monte Carlo simulation, whose results suggest a continuous transition taking place at [Formula: see text]; comparison is also reported with other theoretical treatments, such as Spherical Model, Molecular Field and Two Site Cluster approximations.
Physics Letters A, 2002
The simplest plane rotator model consists of two-component unit vectors, associated with a D-dime... more The simplest plane rotator model consists of two-component unit vectors, associated with a D-dimensional lattice (say ZD), parameterized by polar angles ϕj, and interacting via a ferromagnetic potential restricted to nearest neighbours U=Ujk=−ϵcos(ϕj−ϕk); here ϵ is a positive quantity setting energy and temperature scales (i.e., T∗=kBT/ϵ). On the other hand, the xy model involves three-component unit vectors, parameterized by polar
Physical Review E, 1997
The undercooling effect on the phase-ordering dynamics of nematic liquid crystals is considered. ... more The undercooling effect on the phase-ordering dynamics of nematic liquid crystals is considered. We assume the nematic liquid crystal to have a scalar order parameter, and also suppose the system to be isothermal and initially temperature-quenched into the metastable regime of the isotropic phase. Based on planar domain wall solutions of the time-dependent Ginzburg-Landau equation, Bray and Humayun's theory of phase-ordering dynamics is generalized to include the undercooling effect on the late stage of growth.
Journal of the Chemical Society, Faraday Transactions 2, 1979
ABSTRACT
Il Nuovo Cimento D, 1988
Summary We consider a classical, system, consisting of two-dimensional unit vectors associated w... more Summary We consider a classical, system, consisting of two-dimensional unit vectors associated with a one-dimensional lattice {uk|k∈Z} and interacting via translationally invariant pair potential(s)$$W_m = - \varepsilon \left| {j - k} \right|^{ - s} T_m (u_j \cdot u_k ), \varepsilon > 0,s > 1;$$heremis a positive integer,TTmis a Tchebyshev polynomial of the first kind:$$T_m (u_j \cdot u_k ) = \cos [m(\varphi _j - \varphi _k )],$$and {ϕk} are the angles defining the orientations of the plane rotators in an arbitrary reference frame. For a givens, all the potential modelsWmhave the same partition function, and several averages can be defined in a way independent ofm; the system has been proven rigorously to possess an orientationally ordered phase stable at low but finite temperature when 1ss≥2. This theorem also holds for the corresponding classical Heisenberg and spherical models, whereas, in the Ising model, the ordered phase survives for 1s≤2. We report here Monte Carlo simulation results for the borderline case defined bys=2, and compare with its exactly solvable nearest-neighbour counterpart. The correlation functions show a significant amount of short- and intermediate-range orientational order, which decays slowly with temperature. The simulated system exhibits spontaneous ordering setting in atT*≤1.15, and this may conceivably reflect the conjectured transition to a phase with infinite susceptibility.
Physics Letters A, 2004
The present Letter considers a biaxial nematogenic lattice model, involving particles of D2h symm... more The present Letter considers a biaxial nematogenic lattice model, involving particles of D2h symmetry, whose centres of mass are associated with a 3-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbours.Let the two orthonormal triads {uj,j=1,2,3} and {vk,k=1,2,3} define orientations of a pair of interacting particles, and let Gjk=P2(vj⋅uk), where P2(⋯) denotes the
![Research paper thumbnail of Erratum: Minimal coupling model of the biaxial nematic phase [Phys. Rev. E 71, 051714 (2005)]](https://attachments.academia-assets.com/108843205/thumbnails/1.jpg)
](![Research paper thumbnail of Erratum: Orientationally ordered phase produced by fully antinematic interactions: A simulation study [Phys. Rev. E 84, 011703 (2011)]](https://attachments.academia-assets.com/108843202/thumbnails/1.jpg)
](![Research paper thumbnail of Publisher's Note: Antinematic orientational order produced by an extreme case of the generalized Straley lattice model [Phys. Rev. E 86, 020702(R) (2012)]](https://attachments.academia-assets.com/108843204/thumbnails/1.jpg)
](Physical Review E, 2013
with an error in the Acknowledgments on page 4. On page 4, the second to last sentence in the las... more with an error in the Acknowledgments on page 4. On page 4, the second to last sentence in the last paragraph should read as "F. B. wishes to acknowledge MIUR PRIN 2009 national project 'Novel ordered systems for high response molecular devices' for financial support." The paper has been corrected as of 11 September 2013. The text is incorrect in the printed version of the journal.
The European Physical Journal D, 2004
Models for the mutual potential energy between two molecules proposed in the scientific literatur... more Models for the mutual potential energy between two molecules proposed in the scientific literature often contain a sum of inverse-power interactions involving pairs of sites belonging to the two particles; in turn, these quantities are functions of a few scalar invariants involved in the problem at hand, and one is often interested in directly obtaining an explicit expression of the potential in terms of the latter; the extensively studied two-centre multipole expansion for the mutual electrostatic energy between two charge distributions is a well-known example of this procedure and of its restrictions. We consider here another, less widely known and possibly complementary, approach, proposed byŠebek some years ago [J. Sebek, Czech. J. Phys. B 38, 1185 (1988)]; the resulting formulae show that this procedure can become computationally favourable for sufficiently high molecular symmetry.
Zeitschrift Naturforschung Teil a, 1974
Physical Review E, 2007
Over the last few years, renewed interest has been raised by the simplified general interaction m... more Over the last few years, renewed interest has been raised by the simplified general interaction models proposed by Straley for mesogenic molecules possessing the D 2h symmetry and capable of producing biaxial nematic order. It has already been shown that, in the presence of certain special symmetries, just two out of the four order parameters that are in general necessary, suffice for the description of a biaxial phase. For some other range of parameters, these reducing symmetries do not hold, and, moreover, a mean-field treatment has to be suitably changed into a minimax strategy, still producing a transition to a low-temperature biaxial phase. Upon studying the general parameter range, we identify as a common feature the behavior of a uniaxial order parameter, attaining a local minimum at the biaxial-to-uniaxial transition temperature, and recognizably increasing away from it. This finding is confirmed by a Monte Carlo simulation.
Physica A: Statistical Mechanics and its Applications, 2003
By now, nematogenic lattice models have been extensively studied in the literature dealing with l... more By now, nematogenic lattice models have been extensively studied in the literature dealing with liquid crystals; they usually involve cylindrically symmetric (uniaxial) particles and pairwise additive interaction potentials. On the other hand, quantum mechanical perturbation theory shows that interatomic or intermolecular potentials are only approximately pairwise additive; the pairwise additivity approximation (PAA) of molecular interactions has been extensively and systematically
Physical Review B, 1993
The present paper considers a classical system, consisting of n-component unit vectors (n = 2, 3)... more The present paper considers a classical system, consisting of n-component unit vectors (n = 2, 3), associated with a one-dimensional lattice (uz~k C Z), and interacting via a translationally invariant pair potential of the long-range, antiferromagnetic and anisotropic form W = W~A, +e~j-k~(au~, "uq"+,6 gz u~, quq, q). Here e is a positive quantity setting energy and temperature scales (i.e., T* = ksT/e), a and b are positive numbers, and uq, g denotes the Cartesian components of the unit vectors, Available rigorous results exclude the existence of order at finite temperature in the isotropic case a = b, whereas spin-wave arguments imply its existence in the anisotropic one a)b & 0, for which no such theorems are known; we report here a simulation study of the extremely anisotropic case a = 1, b = 0. Results obtained over a range of sample sizes suggested the existence of antiferromagnetic order in the thermodynamic limit at finite temperature; we have estimated the transition temperatures to be T, * = 0.19 + 0.01 (n = 2) and T; = 0.15 + 0.01 (n = 3).
Physical Review B, 1990
We consider a classical system, consisting of two-component unit vectors I u"j, associated with a... more We consider a classical system, consisting of two-component unit vectors I u"j, associated with a square lattice, and interacting via translationally and rotationally invariant pair potentials of the long-range and ferromagnetic form W= W, &=-e~x,-xk~u, ul"e&0, p&2, where xi, are the coordinates of the lattice sites, Combining available theoretical results, one can conclude that for all p~4 the system disorders at all finite temperatures and exhibits a transition to a lowtemperature phase with infinite susceptibility (Kosterlitz-Thouless-like transition); theoretical bounds on the transition temperature can also be obtained. We report here Monte Carlo simulation results for the potential model defined by p=4 and estimate its transition temperature to be T, *4 =2.23+0. 03, where T*= kz T/c.
International Journal of Modern Physics B, 1998
Director configurations in nematic Liquid Crystals can be determined by minimizing their elastic ... more Director configurations in nematic Liquid Crystals can be determined by minimizing their elastic free-energy density, on the basis of elastic constants and of specific boundary conditions; in some published cases, this has been obtained by numerical procedures where the elastic free-energy density plays the same role as the overall potential energy in a standard Monte Carlo simulation. The "potentials" used in these papers are short-ranged but, in general, not pairwise additive, unless the three elastic constants are set to a common value, thus reducing the potential to the well-known Lebwohl–Lasher lattice model.On the other hand, one can construct, possibly in different ways, a lattice model with pairwise additive interactions, approximately reproducing the elastic free-energy density, where parameters defining the pair potential are expressed as linear combinations of elastic constants; a nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess (...
International Journal of Modern Physics B, 1996
We have considered a classical spin system, consisting of n-component unit vectors (n = 2, 3), as... more We have considered a classical spin system, consisting of n-component unit vectors (n = 2, 3), associated with a semi-infinite lattice in one dimension {uk, k ∈ N+}, and interacting via inhomogeneous pair potentials, in general anisotropic in spin space, and of the long-range ferromagnetic form [Formula: see text] here ∊ is a positive constant setting energy and temperature scales (i.e. T* = k B T/∊), a ≥ 0, b ≥ 0, and the symbols uj, α denote cartesian components of the spins. For some specific values of the two parameters a and b, and on the basis of available theoretical results, one can prove the existence of an ordering transition taking place at finite temperature, and obtain rigorous upper and lower bounds on the transition temperatures. This holds, for example, when n = 2, 3, a > b = 0 (the models studied in our previous paper), as well as for n = 2, a = b > 0 and n = 3, b > a = 0, where a continuous O(2) symmetry of the interaction is involved. We have studied thes...
International Journal of Modern Physics B, 1999
We have considered a classical lattice-gas model, consisting of a two-dimensional lattice Z2, eac... more We have considered a classical lattice-gas model, consisting of a two-dimensional lattice Z2, each site of which hosts at most one two-component unit vector; particles occupying pairs of nearest-neighbouring sites interact via the ferromagnetic potential [Formula: see text] where νj=0,1 denotes occupation numbers, uj are the unit vectors (classical spins) and ∊ is a positive constant setting energy and temperature scales; the total Hamiltonian is given by [Formula: see text] where ∑{j
International Journal of Modern Physics B, 1996
We have considered a classical spin system, consisting of 3-component unit vectors, associated wi... more We have considered a classical spin system, consisting of 3-component unit vectors, associated with a two-dimensional lattice {uk, k ∈ Z2}, and interacting via a translationally and rotationally invariant pair potential, of the long-range ferromagnetic form [Formula: see text] Here ∊ is a positive constant setting energy and temperature scales (i.e. T* = k B T/∊), and xj denotes dimensionless coordinates of the lattice sites. This potential model is known rigorously to possess an ordering transition at finite temperature, and has been characterized quantitatively by Monte Carlo simulation, whose results suggest a continuous transition taking place at [Formula: see text]; comparison is also reported with other theoretical treatments, such as Spherical Model, Molecular Field and Two Site Cluster approximations.
Physics Letters A, 2002
The simplest plane rotator model consists of two-component unit vectors, associated with a D-dime... more The simplest plane rotator model consists of two-component unit vectors, associated with a D-dimensional lattice (say ZD), parameterized by polar angles ϕj, and interacting via a ferromagnetic potential restricted to nearest neighbours U=Ujk=−ϵcos(ϕj−ϕk); here ϵ is a positive quantity setting energy and temperature scales (i.e., T∗=kBT/ϵ). On the other hand, the xy model involves three-component unit vectors, parameterized by polar
Physical Review E, 1997
The undercooling effect on the phase-ordering dynamics of nematic liquid crystals is considered. ... more The undercooling effect on the phase-ordering dynamics of nematic liquid crystals is considered. We assume the nematic liquid crystal to have a scalar order parameter, and also suppose the system to be isothermal and initially temperature-quenched into the metastable regime of the isotropic phase. Based on planar domain wall solutions of the time-dependent Ginzburg-Landau equation, Bray and Humayun's theory of phase-ordering dynamics is generalized to include the undercooling effect on the late stage of growth.
Journal of the Chemical Society, Faraday Transactions 2, 1979
ABSTRACT
Il Nuovo Cimento D, 1988
Summary We consider a classical, system, consisting of two-dimensional unit vectors associated w... more Summary We consider a classical, system, consisting of two-dimensional unit vectors associated with a one-dimensional lattice {uk|k∈Z} and interacting via translationally invariant pair potential(s)$$W_m = - \varepsilon \left| {j - k} \right|^{ - s} T_m (u_j \cdot u_k ), \varepsilon > 0,s > 1;$$heremis a positive integer,TTmis a Tchebyshev polynomial of the first kind:$$T_m (u_j \cdot u_k ) = \cos [m(\varphi _j - \varphi _k )],$$and {ϕk} are the angles defining the orientations of the plane rotators in an arbitrary reference frame. For a givens, all the potential modelsWmhave the same partition function, and several averages can be defined in a way independent ofm; the system has been proven rigorously to possess an orientationally ordered phase stable at low but finite temperature when 1ss≥2. This theorem also holds for the corresponding classical Heisenberg and spherical models, whereas, in the Ising model, the ordered phase survives for 1s≤2. We report here Monte Carlo simulation results for the borderline case defined bys=2, and compare with its exactly solvable nearest-neighbour counterpart. The correlation functions show a significant amount of short- and intermediate-range orientational order, which decays slowly with temperature. The simulated system exhibits spontaneous ordering setting in atT*≤1.15, and this may conceivably reflect the conjectured transition to a phase with infinite susceptibility.
Physics Letters A, 2004
The present Letter considers a biaxial nematogenic lattice model, involving particles of D2h symm... more The present Letter considers a biaxial nematogenic lattice model, involving particles of D2h symmetry, whose centres of mass are associated with a 3-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbours.Let the two orthonormal triads {uj,j=1,2,3} and {vk,k=1,2,3} define orientations of a pair of interacting particles, and let Gjk=P2(vj⋅uk), where P2(⋯) denotes the
Physical Review E, 2013
with an error in the Acknowledgments on page 4. On page 4, the second to last sentence in the las... more with an error in the Acknowledgments on page 4. On page 4, the second to last sentence in the last paragraph should read as "F. B. wishes to acknowledge MIUR PRIN 2009 national project 'Novel ordered systems for high response molecular devices' for financial support." The paper has been corrected as of 11 September 2013. The text is incorrect in the printed version of the journal.