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Papers by A. Klíč

Research paper thumbnail of Ergodicity breaking in frustrated disordered systems: replicas in mean-field spin-glass models

Phase Transitions, 2014

We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry ... more We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry of the Hamiltonian and present a way how to amend it in the low-temperature phase. We demonstrate this phenomenon on mean-field models of spin glasses. We use replicas of the spin variables to test thermodynamic homogeneity of ergodic equilibrium systems. We show that replicasymmetry breaking reflects ergodicity breaking and is used to restore an ergodic state. We then present explicit asymptotic solutions for the Ising, Potts and p-spin glasses. Each of the models shows a different low-temperature behavior and the way the replica symmetry and ergodicity are broken.

Research paper thumbnail of Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature

Physical Review B, 2006

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a s... more We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.

Research paper thumbnail of Mean-field solution of the Potts glass near the transition temperature to the ordered phase

Physical Review B, 2011

We expand asymptotically mean-field solutions of the p < 4 Potts glass with various levels of rep... more We expand asymptotically mean-field solutions of the p < 4 Potts glass with various levels of replica-symmetry breaking below the transition temperature to the glassy phase. We find that the ordered phase is degenerate and solutions with one hierarchy of spin replicas and with the full continuous replica-symmetry breaking coexist for p > p * ≈ 2.82. The latter emerges immediately with the instability of the replica-symmetric one. Apart from these two solutions there exists also a succession of unstable states converging to the solution with the continuous replica-symmetry breaking that is marginally stable and has the highest free energy.

Research paper thumbnail of Origin of the linear term in the pseudo-spin Hamiltonian of compositionally graded ferroelectrics

Journal of Electroceramics, 2008

ABSTRACT This paper is devoted to the microscopic theory of compositionally graded ferroelectrics... more ABSTRACT This paper is devoted to the microscopic theory of compositionally graded ferroelectrics (CGF). From a simple microscopic picture of CGF we deduce the so called transverse Ising pseudo-spin model. However the Hamiltonian used in recent papers does not contain a linear term in pseudo-spins. We show that for inhomogeneous material it is necessary to modify the Ising Hamiltonian by addition of the linear term in pseudo-spins. This linear term is equivalent to introduction of an external bias field. The influence of long-range forces is discussed.

Research paper thumbnail of Nonergodic behavior of the phi4,phi3-lattice model

Czechoslovak Journal of Physics - CZECH J PHYS, 1998

We investigated a model of harmonically coupled oscillators placed in an asymmetric double-well p... more We investigated a model of harmonically coupled oscillators placed in an asymmetric double-well potential of the varphi4,varphi3 type. This model can be a good candidate for the description of pyroelectric crystalline materials. According to the model the system is in a nonergodic state in a certain range of temperatures.

Research paper thumbnail of Replica-symmetry breaking: discrete and continuous schemes in the Sherrington–Kirkpatrick model

Journal of Physics A: Mathematical and Theoretical, 2008

We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model.... more We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the continuous solution. The general analysis is accompanied by an explicit asymptotic solution near the de Almeida-Thouless instability line in the nonzero magnetic field.

Research paper thumbnail of Ergodicity breaking in frustrated disordered systems: replicas in mean-field spin-glass models

Phase Transitions, 2014

We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry ... more We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry of the Hamiltonian and present a way how to amend it in the low-temperature phase. We demonstrate this phenomenon on mean-field models of spin glasses. We use replicas of the spin variables to test thermodynamic homogeneity of ergodic equilibrium systems. We show that replicasymmetry breaking reflects ergodicity breaking and is used to restore an ergodic state. We then present explicit asymptotic solutions for the Ising, Potts and p-spin glasses. Each of the models shows a different low-temperature behavior and the way the replica symmetry and ergodicity are broken.

Research paper thumbnail of Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature

Physical Review B, 2006

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a s... more We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.

Research paper thumbnail of Mean-field solution of the Potts glass near the transition temperature to the ordered phase

Physical Review B, 2011

We expand asymptotically mean-field solutions of the p < 4 Potts glass with various levels of rep... more We expand asymptotically mean-field solutions of the p < 4 Potts glass with various levels of replica-symmetry breaking below the transition temperature to the glassy phase. We find that the ordered phase is degenerate and solutions with one hierarchy of spin replicas and with the full continuous replica-symmetry breaking coexist for p > p * ≈ 2.82. The latter emerges immediately with the instability of the replica-symmetric one. Apart from these two solutions there exists also a succession of unstable states converging to the solution with the continuous replica-symmetry breaking that is marginally stable and has the highest free energy.

Research paper thumbnail of Origin of the linear term in the pseudo-spin Hamiltonian of compositionally graded ferroelectrics

Journal of Electroceramics, 2008

ABSTRACT This paper is devoted to the microscopic theory of compositionally graded ferroelectrics... more ABSTRACT This paper is devoted to the microscopic theory of compositionally graded ferroelectrics (CGF). From a simple microscopic picture of CGF we deduce the so called transverse Ising pseudo-spin model. However the Hamiltonian used in recent papers does not contain a linear term in pseudo-spins. We show that for inhomogeneous material it is necessary to modify the Ising Hamiltonian by addition of the linear term in pseudo-spins. This linear term is equivalent to introduction of an external bias field. The influence of long-range forces is discussed.

Research paper thumbnail of Nonergodic behavior of the phi4,phi3-lattice model

Czechoslovak Journal of Physics - CZECH J PHYS, 1998

We investigated a model of harmonically coupled oscillators placed in an asymmetric double-well p... more We investigated a model of harmonically coupled oscillators placed in an asymmetric double-well potential of the varphi4,varphi3 type. This model can be a good candidate for the description of pyroelectric crystalline materials. According to the model the system is in a nonergodic state in a certain range of temperatures.

Research paper thumbnail of Replica-symmetry breaking: discrete and continuous schemes in the Sherrington–Kirkpatrick model

Journal of Physics A: Mathematical and Theoretical, 2008

We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model.... more We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the continuous solution. The general analysis is accompanied by an explicit asymptotic solution near the de Almeida-Thouless instability line in the nonzero magnetic field.

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