Related papers: Shape dependent finite-size effect of critical two…
There is no an exact solution to three-dimensional (3D) finite-size Ising model (referred to as the Ising model hereafter for simplicity) and even two-dimensional (2D) Ising model with non-zero external field to our knowledge. Here by using…
The Ising model at inverse temperature $\beta$ and zero external field can be obtained via the Fortuin-Kasteleyn (FK) random-cluster model with $q=2$ and density of open edges $p=1-e^{-\beta}$ by assigning spin +1 or -1 to each vertex in…
We demonstrate that the Ising model on a general triangular graph with 3 distinct couplings $K_1,K_2,K_3$ corresponds to an affine transformed conformal field theory (CFT). Full conformal invariance of the $c= 1/2$ minimal CFT is restored…
We describe results of the cluster algorithm Special Purpose Processor simulations of the 2D Ising model with impurity bonds. Use of large lattices, with the number of spins up to $10^6$, permitted to define critical region of temperatures,…
We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the…
We study equilibrium as well as dynamical properties of the finite-size fully connected Ising model with a transverse field at the zero temperature. In relation to the equilibrium, we present approximate ground and first excited states that…
Simulation data are analyzed for four 3D spin-$1/2$ Ising models: on the FCC lattice, the BCC lattice, the SC lattice and the Diamond lattice. The observables studied are the susceptibility, the reduced second moment correlation length, and…
We analyze exact ground-state energies of two-dimensional Ising spin glasses with either Gaussian or bimodal nearest-neighbor interactions for large system sizes and for three types of boundary conditions: free on both axes, periodic on…
The Ising spin - S model on recursive p - polygonal structures in the external magnetic field is considered and the general form of the free energy and magnetization for arbitrary spin is derived. The exact relation between the free…
It is known that the Ising model on $\mathbb {Z}^d$ at a given temperature is a finitary factor of an i.i.d. process if and only if the temperature is at least the critical temperature. Below the critical temperature, the plus and minus…
We study the behaviour of a universal combination of susceptibility and correlation length in the Ising model in two and three dimensions, in presence of both magnetic and thermal perturbations, in the neighbourhood of the critical point.…
We reconsider the criticality of the Ising model on two-dimensional dynamical triangulations based on the $N \times N$ hermitian two-matrix model with the introduction of a loop-counting parameter and linear terms in the potential. We show…
In this paper, we use the dimer method to obtain the free energy of Ising models consisting of repeated horizontal strips of width $m$ connected by sequences of vertical strings of length $n$ mutually separated by distance $N$, with $N$…
We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the…
Using the strong disorder renormalization group method we study numerically the critical behavior of the random transverse Ising model at a free surface, at a corner and at an edge in D=2, 3 and 4-dimensional lattices. The surface…
The critical behavior of the classical Ising model on a three-dimensional fractal lattice with Hausdorff dimension $d_H = \ln32 / \ln4 = 2.5$ is investigated using the higher-order tensor renormalization group (HOTRG) method. We determine…
We present the results of a finite-size analysis of the four dimensional abelian surface gauge model. This model is defined assigning abelian variables to the plaquettes of an hypercubical lattice, and is dual to the four dimensional Ising…
The paper considers the generalized Ising model in the $2\times2\times\infty$ strip with a Hamiltonian invariant with respect to the central axis of rotation through the angle $\pi/2$, which includes all possible multiplicative interactions…
We obtain the exact physical characteristics of the triple-chain Ising model on a torus with all possible multispin interactions invariant with respect to rotation by the angle $2\pi / 3$. The exact value of the partition function in a…
We investigate relaxation dynamics along the entire first-order phase transition line by analyzing the time evolution of the free energy landscape in the three-dimensional kinetic Ising model. Near the critical temperature $T_{\rm c}$, the…