Des Johnston | Heriot-Watt University (original) (raw)

Papers by Des Johnston

Nuclear Physics B, 2014

ABSTRACT The three-dimensional purely plaquette gonihedric Ising model and its dual are investiga... more ABSTRACT The three-dimensional purely plaquette gonihedric Ising model and its dual are investigated to resolve inconsistencies in the literature for the values of the inverse transition temperature of the very strong temperature-driven first-order phase transition that is apparent in the system. Multicanonical simulations of this model allow us to measure system configurations that are suppressed by more than 60 orders of magnitude compared to probable states. With the resulting high-precision data, we find excellent agreement with our recently proposed nonstandard finite-size scaling laws for models with a macroscopic degeneracy of the low-temperature phase by challenging the prefactors numerically. We find an overall consistent inverse transition temperature of 0.551334(8) from the simulations of the original model both with periodic and fixed boundary conditions, and the dual model with periodic boundary conditions. For the original model with periodic boundary conditions, we obtain the first reliable estimate of the interface tension, 0.12037(18), using the statistics of suppressed configurations.

Physics Procedia, 2014

ABSTRACT It is known that fixed boundary conditions modify the leading finite-size corrections fo... more ABSTRACT It is known that fixed boundary conditions modify the leading finite-size corrections for an L^3 lattice in 3d at a first-order phase transition from 1/L^3 to 1/L. We note that an exponential low-temperature phase degeneracy of the form 23L will lead to a different leading correction of order 1/L^2. A 3d gonihedric Ising model with a four-spin interaction, plaquette Hamiltonian displays such a degeneracy and we confirm the modified scaling behaviour using high-precision multicanonical simulations. We remark that other models such as the Ising antiferromagnet on the FCC lattice, in which the number of “true” low-temperature phases is not macroscopically large but which possess an exponentially degenerate number of low lying states may display an ef- fective version of the modified scaling law for the range of lattice sizes accessible in simulations.

Physical Review Letters, 2014

We note that the standard inverse system volume scaling for finite-size corrections at a firstord... more We note that the standard inverse system volume scaling for finite-size corrections at a firstorder phase transition (i.e., 1/L 3 for an L × L × L lattice in 3D) is transmuted to 1/L 2 scaling if there is an exponential low-temperature phase degeneracy. The gonihedric Ising model which has a four-spin interaction, plaquette Hamiltonian provides an exemplar of just such a system. We use multicanonical simulations of this model to generate high-precision data which provides strong confirmation of the non-canonical finite-size scaling law. The dual to the gonihedric model, which is an anisotropically coupled Ashkin-Teller model, has a similar degeneracy and also displays the non-canonical scaling. PACS numbers: 05.50.+q, 05.70.Jk, 64.60.-i, 75.10.Hk

NATO Science Series: B:, 2002

Four dimensional simplicial gravity has been studied by means of Monte Carlo simulations for some... more Four dimensional simplicial gravity has been studied by means of Monte Carlo simulations for some time1 and an extensive numerical documentation of the properties of the model has been gathered. The main outcome of the studies is that the model undergoes a discontinuous phase transition2 between the elongated and the crumpled phase when one changes the coupling to curvature. In the crumpled phase there are singular vertices in the system having orders growing extensively with the volume of the system3. The Hausdorff ...

Nuclear Physics B, 1995

In a recent paper [1] we found strong evidence from simulations that the Ising antiferromagnet on... more In a recent paper [1] we found strong evidence from simulations that the Ising antiferromagnet on "thin" random graphs -Feynman diagrams -displayed a mean-field spin glass transition. The intrinsic interest of considering such random graphs is that they give mean field theory results without long range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice or in previous replica calculations.

Nuclear Physics B, 2015

In this paper we conduct a careful multicanonical simulation of the isotropic 3d plaquette ("goni... more In this paper we conduct a careful multicanonical simulation of the isotropic 3d plaquette ("gonihedric") Ising model and confirm that a planar, fuki-nuke type order characterises the low-temperature phase of the model. From consideration of the anisotropic limit of the model we define a class of order parameters which can distinguish the low-and hightemperature phases in both the anisotropic and isotropic cases. We also verify the recently voiced suspicion that the order parameter like behaviour of the standard magnetic susceptibility χ m seen in previous Metropolis simulations was an artefact of the algorithm failing to explore the phase space of the macroscopically degenerate low-temperature phase. χ m is therefore not a suitable order parameter for the model.

Physical Review D, 2014

Discretized formulations of 2-form abelian and non-abelian gauge fields on ddimensional hypercubi... more Discretized formulations of 2-form abelian and non-abelian gauge fields on ddimensional hypercubic lattices have been discussed in the past by various authors and most recently in . In this note we recall that the Hamiltonian of a Z2 variant of such theories is one of the family of generalized Ising models originally considered by Wegner . For such "Z2 lattice gerbe theories" general arguments can be used to show that a phase transition for Wilson surfaces will occur for d > 3 between volume and area scaling behaviour. In 3d the model is equivalent under duality to an infinite coupling model and no transition is seen, whereas in 4d the model is dual to the 4d Ising model and displays a continuous transition. In 5d the Z2 lattice gerbe theory is self-dual in the presence of an external field and in 6d it is self-dual in zero external field.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2003

Motivated by the observation that geometrizing statistical mechanics offers an interesting altern... more Motivated by the observation that geometrizing statistical mechanics offers an interesting alternative to more standard approaches, we calculate the scaling behavior of the curvature R of the information geometry metric for the spherical model. We find that R approximately epsilon(-2), where epsilon=beta(c)-beta is the distance from criticality. The discrepancy from the naively expected scaling R approximately epsilon(-3) is explained and compared with that for the Ising model on planar random graphs, which shares the same critical exponents.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

Using Monte Carlo simulations we study crystallization in the three-dimensional Ising model with ... more Using Monte Carlo simulations we study crystallization in the three-dimensional Ising model with four-spin interaction. We monitor the morphology of crystals which grow after placing crystallization seeds in a supercooled liquid. Defects in such crystals constitute an intricate and very stable network that separates various domains by tensionless domain walls. We also show that the crystallization which occurs during the continuous heating of the glassy phase takes place at a heating-rate-dependent temperature.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000

Using Monte Carlo simulations we study cooling-rate effects in a three-dimensional Ising model wi... more Using Monte Carlo simulations we study cooling-rate effects in a three-dimensional Ising model with four-spin interactions. During coarsening, this model develops growing energy barriers, which at low temperature lead to very slow dynamics. We show that the characteristic zero-temperature length increases very slowly with the inverse cooling rate, similarly to the behavior of ordinary glasses. For computationally accessible cooling rates the model undergoes an ideal glassy transition, i.e., the glassy transition for a very small cooling rate coincides with a thermodynamic singularity. We also study the cooling of this model with a certain fraction of spins fixed. Due to such heterogeneous crystallization seeds, the final state strongly depends on the cooling rate. Only for a sufficiently fast cooling rate does the system end up in a glassy state, while slow cooling inevitably leads to a crystal phase.

The KPZ formula shows that coupling central charge c ≤ 1 spin models to 2D quantum gravity dresse... more The KPZ formula shows that coupling central charge c ≤ 1 spin models to 2D quantum gravity dresses the conformal weights to get new critical exponents, where the relation between the original and dressed weights depends only on c. At the discrete level the coupling to 2D gravity is effected by putting the spin models on annealed ensembles of Φ 3 planar random graphs or their dual triangulations, where the connectivity fluctuates on the same time-scale as the spins.

Physical Review D, 1992

We investigate the crumpling transition for a dynamically triangulated random surface embedded in... more We investigate the crumpling transition for a dynamically triangulated random surface embedded in two dimensions using an effective model in which the disordering effect of the X variables on the correlations of the normals is replaced by a long-range "antiferromagnetic" term. We compare the results from a Monte Carlo simulation with those obtained for the standard action which retains the X's and discuss the nature of the phase transition.

Physical Review D, 1994

We investigate actions for dynamically triangulated random surfaces that consist of a gaussian or... more We investigate actions for dynamically triangulated random surfaces that consist of a gaussian or area term plus the modulus of the gaussian curvature and compare their behavior with both gaussian plus extrinsic curvature and "Steiner" actions.

Physical Review D, 1995

It has been shown that it is possible to extract values for critical couplings and γstring in mat... more It has been shown that it is possible to extract values for critical couplings and γstring in matrix models by deriving a renormalization group equation for the variation of the of the free energy as the size N of the matrices in the theory is varied. In this paper we derive a "renormalization group equation" for the Penner model by direct differentiation of the partition function and show that it reproduces the correct values of the critical coupling and γstring and is consistent with the logarithmic corrections present for g = 0, 1.

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 1996

We perform simulations of an absolute value version of the Villain model on φ3 and φ4 Feynman dia... more We perform simulations of an absolute value version of the Villain model on φ3 and φ4 Feynman diagrams,“thin” 3-regular and 4-regular random graphs. The φ4 results are in excellent quantitative agreement with the exact calculations by Dorey and Kurzepa for an annealed ensemble of thin graphs, in spite of simulating only a single graph of each size. We also derive exact results for an annealed ensemble of φ3 graphs and again find excellent agreement with the numerical data for single φ3 graphs. The simulations confirm ...