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The recent progress in the study of finite-size scaling (FSS) properties of the Ising model is briefly reviewed. We calculate the universal FSS functions for the Binder parameter $g$ and the magnetization distribution function $p(m)$ for…
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…
We review recent results concerning finite size corrections to the Ising model free energy on lattices with non-trivial topology and curvature. From conformal field theory considerations two distinct universal terms are expected, a…
We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D…
We study the zeros of the partition function in the complex temperature plane (Fisher zeros) and in the complex external field plane (Lee-Yang zeros) of a frustrated Ising model with competing nearest-neighbor ($J_1 > 0$) and…
A mixed spin-1/2 and spin-3/2 Ising model on a decorated square lattice with a nearest- neighbor interaction, next-nearest-neighbor bilinear interaction, three-site four-spin in- teraction and single-ion anisotropy is exactly investigated…
In this succinct note, it is showed that a partition function of equivalent classes of hyperbolic surfaces can be connected to an Ising model located on the boundary of the Poincare disc, as hinted by Poincare's Uniformization theorem and…
We present a {\it numerically exact} study of the Hubbard model with spin-dependent anisotropic hopping on the square lattice using auxiliary-field quantum Monte Carlo method. At half filling, the system undergoes Ising phase transitions…
The spin - 3/2 Ising model on a square lattice is investigated. It is shown that this model is reducible to an eight - vertex model on a surface in the parameter space spanned by coupling constants J, K, L and M. It is shown that this model…
The Ising model is famous model for magnetic substances in Statistical Physics, and has been greatly studied in many forms. It was solved in one-dimension by Ernst Ising in 1925 and in two-dimensions without an external magnetic field by…
We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group $G$. When $G=SU(2)$, the statistical weight is constructed from the $15j$-symbol as well as the $6j$-symbol for recombination of…
The bulk and boundary magnetizations are calculated for the critical Ising model on a randomly triangulated disk in the presence of a boundary magnetic field h. In the continuum limit this model corresponds to a c = 1/2 conformal field…
A superintegrable, discrete model of the quantum isotropic oscillator in two-dimensions is introduced. The system is defined on the regular, infinite-dimensional $\mathbb{N}\times \mathbb{N}$ lattice. It is governed by a Hamiltonian…
Using exact enumeration, the Casimir amplitude and the Casimir force are calculated for the square lattice Ising model with quenched surface disorder on one surface in cylinder geometry at criticality. The system shape is characterized by…
The influence of a layered aperiodic modulation of the couplings on the critical behaviour of the two-dimensional Ising model is studied in the case of marginal perturbations. The aperiodicity is found to induce anisotropic scaling. The…
An explicit expression for the partition function of two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived by a systematic enumeration of all the spin configurations pertaining to a square lattice of…
The spin-1/2 Ising model on a square lattice, with fluctuating bond interactions between nearest neighbors and in the presence of a random magnetic field, is investigated within the framework of the effective field theory based on the use…
The critical behavior at a corner in two-dimensional Ising and three-state Potts models is studied numerically on the square lattice using transfer operator techniques. The local critical exponents for the magnetization and the energy…
There is no an accepted exact partition function (PF) for the three dimensional (3D) Ising model to our knowledge. Mainly based on the connection between the lattice Green function (LGF) for the simple cubic lattice and that for the…
This paper deals with the partition function of the Ising model from statistical mechanics, which is used to study phase transitions in physical systems. A special case of interest is that of the Ising model with constant energies and…