arXiv subjects

Desmond A. Johnston

Publications and source records attributed to Desmond A. Johnston.

15 recordsLinked to original sources

arXiv2025

Partition Function Zeros of Paths and Normalization Zeros of ASEPS

We exploit the equivalence between the partition function of an adsorbing Dyck walk model and the Asymmetric Simple Exclusion Process (ASEP) normalization to obtain the thermodynamic limit of the locus of the ASEP normalization zeros from a conformal map. We discuss the equivalence between this approach and using an electrostatic analogy to determine the locus, both in the case of the ASEP and the random allocation model.

cond-mat.stat-mech↗

arXiv2024

Yang-Lee zeros for real-space condensation

Using the electrostatic analogy, we derive an exact formula for the limiting Yang-Lee zero distribution in the random allocation model of general weights. This exhibits a real-space condensation phase transition, which is induced by a pressure change. The exact solution allows one to read off the scaling of the density of zeros at the critical point and the angle at which locus of zeros hits the critical point. Since the order of the phase transition and critical exponents can be tuned with a single parameter for several families of weights, the model provides a useful testing ground for verifying various relations between the distribution of zeros and the critical behavior, as well as for exploring the behavior of physical quantities in the mesoscopic regime, i.e., systems of large but finite size. The main result is that asymptotically the Yang-Lee zeros are images of a conformal mapping, given by the generating function for the weights, of uniformly distributed complex phases.

cond-mat.stat-mech↗

arXiv2023

On Random Allocation Models in the Thermodynamic Limit

We discuss the phase transition and critical exponents in the random allocation model (urn model) for different statistical ensembles. We provide a unified presentation of the statistical properties of the model in the thermodynamic limit, uncover new relationships between the thermodynamic potentials and fill some lacunae in previous results on the singularities of these potentials at the critical point and behaviour in the thermodynamic limit. The presentation is intended to be self-contained, so we carefully derive all formulae step by step throughout. Additionally, we comment on a quasi-probabilistic normalisation of configuration weights which has been considered in some recent studies

cond-mat.stat-mech↗

arXiv2023

Rényi Entropy of Zeta-Urns

We calculate analytically the Renyi entropy for the zeta-urn model with a Gibbs measure definition of the micro-state probabilities. This allows us to obtain the singularities in the Rényi entropy from those of the thermodynamic potential, which is directly related to the free energy density of the model. We enumerate the various possible behaviours of the Rényi entropy and its singularities, which depend on both the value of the power law in the zeta-urn and the order of the Rényi entropy under consideration

cond-mat.stat-mech↗

arXiv2020

(Four) Dual Plaquette 3D Ising Models

A characteristic feature of the 3d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3d plaquette Ising and the X-Cube model is similar to that between the 2d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin-Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.

cond-mat.stat-mech↗

arXiv2019

Lattice SUSY for the DiSSEP at $λ^2=1$ (and $λ^2 = -3 $)

We investigate whether the dynamical lattice supersymmetry discussed for various Hamiltonians, including one-dimensional quantum spin chains, by Fendley et.al. and Hagendorf et.al. might also exist for the Markov matrices of any one-dimensional exclusion processes, since these can be related by conjugation to quantum spin chain Hamiltonians. We find that the DiSSEP (Dissipative Symmetric Simple Exclusion Process), introduced by Crampe et.al. provides one such example for suitably chosen parameters. The DiSSEP Markov matrix admits the supersymmetry in these cases because it is conjugate to spin chain Hamiltonians which also possess the supersymmetry. We note that the length-changing supersymmetry relation for the DiSSEP Markov matrix and the supercharge is reminiscent of a "transfer matrix" symmetry that has been observed in other exclusion processes and discuss the similarity.

cond-mat.stat-mech↗

arXiv2016

Plaquette Ising models, degeneracy and scaling

We review some recent investigations of the 3d plaquette Ising model. This displays a strong first-order phase transition with unusual scaling properties due to the size-dependent degeneracy of the low-temperature phase. In particular, the leading scaling correction is modified from the usual inverse volume behaviour 1/L^3 to 1/L^2. The degeneracy also has implications for the magnetic order in the model which has an intermediate nature between local and global order and gives rise to novel fracton topological defects in a related quantum Hamiltonian.

cond-mat.stat-mech↗

arXiv2016

Exact solutions to plaquette Ising models with free and periodic boundaries

An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (Phys. Rev. Lett. 28 (1972) 507), who later dubbed it the fuki-nuke, or "no-ceiling", model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (Phys. Rev. B 81 (2010) 184303). We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.

cond-mat.stat-mech↗

arXiv2015

Macroscopic Degeneracy and order in the 3d plaquette Ising model

The purely plaquette 3d Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, "fuki-nuke" order still exists and we confirm this with multicanonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analysing our measurements.

cond-mat.stat-mech↗

arXiv2015

Planar ordering in the plaquette-only gonihedric Ising model

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 high-temperature 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.

cond-mat.stat-mech↗

arXiv2014

Transmuted finite-size scaling at first-order phase transitions

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 2^3L 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 effective version of the modified scaling law for the range of lattice sizes accessible in simulations.

cond-mat.stat-mech↗

arXiv2014

Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual

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.

cond-mat.stat-mech↗

arXiv2014

$\mathbb{Z}_2$ Lattice Gerbe Theory

$2$-form abelian and non-abelian gauge fields on $d$-dimensional hypercubic lattices have been discussed in the past by various authors and most recently by Lipstein and Reid-Edwards. In this note we recall that the Hamiltonian of a $\mathbb{Z}_2$ variant of such theories is one of the family of generalized Ising models originally considered by Wegner. For such "$\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ lattice gerbe theory is self-dual in the presence of an external field and in $6d$ it is self-dual in zero external field.

cond-mat.stat-mech↗

arXiv2014

Non-Standard Finite-Size Scaling at First-Order Phase Transitions

We note that the standard inverse system volume scaling for finite-size corrections at a first-order phase transition (i.e., 1/L^3 for an L x L x 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-standard 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-standard scaling.

cond-mat.stat-mech↗

arXiv1999

Non-Self Averaging in Autocorrelations for Potts Models on Quenched Random Gravity Graphs

We investigate the non-self-averaging properties of the dynamics of Ising, 4-state Potts and 10-state Potts models in single-cluster Monte Carlo simulations on quenched ensembles of planar, trivalent Phi3 random graphs, which we use as an example of relevant quenched connectivity disorder. We employ a novel application of scaling techniques to the cumulative probability distribution of the autocorrelation times for both the energy and magnetisation in order to discern non-self-averaging. Although the specific results discussed here are for quenched random graphs, the method has quite general applicability.

cond-mat.stat-mech↗