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Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…
We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of zero external magnetic field, using a generalization of the combinatorial method of Feynman and…
A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D…
We consider the Ising model on the hexagonal lattice evolving according to Metropolis dynamics. We study its metastable behavior in the limit of vanishing temperature when the system is immersed in a small external magnetic field. We…
We examine in detail the theoretical foundations of striking long-range couplings emerging in arrays of fluid cells connected by narrow channels by using a lattice gas (Ising model) description of a system. We present a reexamination of the…
We study classical Ising spin-$\frac{1}{2}$ models on the 2D square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin…
Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…
We consider the two-dimensional $\mathbb{Z}_{2}$ Ising gauge theory coupled to fermionic matter. In absence of electric fields, we prove that, at half-filling, the ground state of the gauge theory coincides with the $\pi$-flux phase,…
An effective field theory exists describing a very large class of biophysically interesting Coulomb gas systems: the lowest order (mean-field) version of this theory takes the form of a generalized Poisson-Boltzmann theory. Interaction…
This paper is our progress report on the project "Ising spectroscopy", devoted to systematic study of the mass spectrum of particles in 2D Ising Field Theory in a magnetic field. Here we address the low-temperature regime, and develop…
This paper provides an introduction to the Stein method framework in the context of steady-state diffusion approximations. The framework consists of three components: the Poisson equation and gradient bounds, generator coupling, and moment…
The two-dimensional Ising model is representable as a lattice free-fermion field theory in terms of the integral over anticommuting Grassmann variables. The exact solution in a zero magnetic field then follows by evaluating Gaussian…
Using a combinatorial method, the partition functions for two-dimensional nearest neighbour Ising models have been derived for a square lattice of 16 sites in the presence of the magnetic field. A novel hierarchical method of enumeration of…
A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of a Ising model defined on the same lattice suggests an approximate expression for the microcanonical…
The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in…
We study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing…
We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The…
We show by a surprisingly simple argument that the exchangeability condition, which is key to the exchangeable pair approach in Stein's method for distributional approximation, can be omitted in many standard settings. This is achieved by…
We calculate the two-point correlation function and magnetic susceptibility in the anisotropic 2D Ising model on a lattice with one infinite and the other finite dimension, along which periodic boundary conditions are imposed. Using exact…
We consider the Ising model on a supercritical Galton-Watson tree $\mathbf{T}_n$ of depth $n$ with a sparse random external field, given by a collection of i.i.d. Bernouilli random variables with vanishing parameter $p_n$. This may me…