相关论文: The critical Z-invariant Ising model via dimers: l…

In this exposition, we consider the dimer problem on an infinite square lattice with partially non-periodic edge weights, which we refer to as the square lattice with interface. In particular, we compute an exact integral form of the…

We investigate the dynamic critical exponent of the two-dimensional Ising model defined on a curved surface with constant negative curvature. By using the short-time relaxation method, we find a quantitative alteration of the dynamic…

Recently, it has been shown that, when the dimension of a graph turns out to be infinite dimensional in a broad sense, the upper critical surface and the corresponding critical behavior of an arbitrary Ising spin glass model defined over…

This paper provides a comprehensive study of the dimer model on infinite minimal graphs with Fock's elliptic weights [arXiv:1503.00289]. Specific instances of such models were studied in [arXiv:052711, arXiv:1612.09082, arXiv1801.00207]; we…

Numerical methods are used to examine the thermodynamic characteristics of the two-dimensional Ising model as a function of the number of spins N. Onsager's solution is generalized to a finite-size lattice, and experimentally validated…

We study planar "vertex" models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including dimer model, and 1-2 model, which we will define. We express the local…

The Ashkin-Teller model can be formulated as a pair of 2D Ising models, interacting via a four-spin interaction. I consider the case of weak anisotropy (slight a-symmetry between the two Ising layers) and weak coupling. I show that the…

A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…

We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer…

We consider the dimer model on the Aztec diamond with Fock's weights, which is gauge equivalent to the model with any choice of positive weight function. We prove an explicit, compact formula for the inverse Kasteleyn matrix, thus extending…

Using recent results in mathematics, I point out that free energies and scale-dependent central charges away from criticality can be represented in compact form where modular invariance is manifest. The main example is the near-critical…

We present analytical results for the strongly anisotropic random field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average…

We study a model of fully-packed dimer configurations (or perfect matchings) on a bipartite periodic graph that is two-dimensional but not planar. The graph is obtained from $\mathbb Z^2$ via the addition of an extensive number of extra…

We study the off-equilibrium critical dynamics of the three dimensional diluted Ising model. We compute the dynamical critical exponent $z$ and we show that it is independent of the dilution only when we take into account the…

It is shown that dimers is Yang-Baxter integrable as a six-vertex model at the free-fermion point with crossing parameter $\lambda=\tfrac{\pi}{2}$. A one-to-many mapping of vertex onto dimer configurations allows the free-fermion solutions…

We prove universality of spin correlations in the scaling limit of the planar Ising model on isoradial graphs with uniformly bounded angles and Z-invariant weights. Specifically, we show that in the massive scaling limit, i.e., as the mesh…

In this work we performed numerical simulations for the Ising model on three dimensional lattices with coordination number equal 5. With Monte Carlo simulations in the static case we evaluated the critical temperature and the static…

We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and…

We show that the two-dimensional $\mathbb{Z}_2$ invariant for time-reversal invariant insulators can be formulated in terms of the boundary-condition dependence of the ground state wavefunction for both non-interacting and…

We show that it is possible to determine the locus of Fisher zeroes in the thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs and their dual quadrangulations by matching up the real part of the high and low…