Related papers: Lace expansion for the Ising model
We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for…
We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain $T \to T_c$, $H \to 0$. The analysis is based on numerical data obtained through the Truncated Free Fermion Space…
The 1-arm exponent $\rho$ for the ferromagnetic Ising model on $\mathbb{Z}^d$ is the critical exponent that describes how fast the critical 1-spin expectation at the center of the ball of radius $r$ surrounded by plus spins decays in powers…
We prove Ornstein-Zernike behavior for the large-distance asymptotics of the two-point function of the Ising model above the critical temperature under essentially optimal assumptions on the interaction. The main contribution of this work…
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field…
In order to investigate the effects of connectivity and proximity in the specific heat, a special class of exactly solvable planar layered Ising models has been studied in the thermodynamic limit. The Ising models consist of repeated…
Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising Spin Glass (ISG) models in dimension two…
The method for calculation of the correlation functions of the Ising-type systems with short-range interaction and with arbitrary value of spin is developed within cluster approximation. For the Ising model (spin $S^z=\pm1$) the expressions…
Starting from the five-loop renormalization-group expansions for the two-dimensional Euclidean scalar \phi^4 field theory (field-theoretical version of two-dimensional Ising model), pseudo-\epsilon expansions for the Wilson fixed point…
The multicritical behavior at the Nishimori point of two-dimensional Ising spin glasses is investigated by using numerical transfer-matrix methods to calculate probability distributions $P(C)$ and associated moments of spin-spin correlation…
The Ising model on ``thin'' graphs (standard Feynman diagrams) displays several interesting properties. For ferromagnetic couplings there is a mean field phase transition at the corresponding Bethe lattice transition point. For…
We defined exponential maps with one parameter, associated with geodesics on the parameter surface. By group theory we proposed a formula of the critical points, which is a direct sum of the Lie subalgebras at the critical temperature. We…
Using a renormalized linked-cluster-expansion method, we have extended to order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on the sc and…
This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph $G$ and the set of non-backtracking walks on $G$. The techniques used also give formulas for spin-spin…
An exact expression for the spin-spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spin-spin…
We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as $\sim r^{-a}$. Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the…
The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition,…
From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scaling scheme involving a set of scaling formulae which express to leading order the temperature (T) and the…
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the spin-1 Ising model on the square lattice. A new formalism is described that…
The Ising model was originally developed to model magnetisation of solids in statistical physics. As a network of binary variables with the probability of becoming 'active' depending only on direct neighbours, the Ising model appears…