Related papers: Ground state numerical study of the three-dimensio…
We study the one dimensional Ising model with ferromagnetic, long range interaction which decays as |i-j|^{-2+a}, 1/2< a<1, in the presence of an external random filed. we assume that the random field is given by a collection of independent…
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.…
The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…
Exact ground states are calculated with an integer optimization algorithm for two and three dimensional site-diluted Ising antiferromagnets in a field (DAFF) and random field Ising ferromagnets (RFIM). We investigate the structure and the…
Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the…
We study random field Ising model on $\mathbb Z^2$ where the external field is given by i.i.d.\ Gaussian variables with mean zero and positive variance. We show that at zero temperature the effect of boundary conditions on the magnetization…
The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical…
Adapting the recent argument of Aizenman, Duminil-Copin and Sidoravicius for the classical Ising model, it is shown here that the magnetization in the transverse-field Ising model vanishes at the critical point. The proof applies to the…
We use Monte Carlo simulations to study a dynamically triangulated disk with Ising spins on the vertices and a boundary magnetic field. For the case of zero magnetic field we show that the model possesses three phases. For one of these the…
Demagnetization, commonly employed to study ferromagnets, has been proposed as the basis for an optimization tool, a method to find the ground state of a disordered system. Here we present a detailed comparison between the ground state and…
We study the ferromagnetic transverse-field Ising model with quenched disorder at $T = 0$ in one and two dimensions by means of stochastic series expansion quantum Monte Carlo simulations using a rigorous zero-temperature scheme. Using a…
We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with $N$ nodes and $N^{\gamma}$ edges, with $1 < \gamma \leq 2$. By conveniently rescaling the coupling constant, the free…
The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality:…
Systems with quenched disorder possess complex energy landscapes that are challenging to explore under the conventional Monte Carlo method. In this work, we implement an efficient entropy sampling scheme for accurate computation of the…
Using Monte Carlo techniques and a star-triangle transformation, Ising models with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on a square lattice with a (1,1) surface are studied near the phase transition. Both…
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…
In this note we study the mean field equations for the $3d$ Random Field Ising Model. We discuss the phase diagram of the model, and we address the problem of finding if such equations admit more than one solution. We find two different…
We investigate the Ising model in one, two, and three dimensions using a cumulant method that allows us to determine the Lee-Yang zeros from the magnetization fluctuations in small lattices. By doing so with increasing system size, we are…
Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In…
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation…