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The selfconsistent approach to the 2D Ising Model with quenched random bonds is extended to the full lattice theory of four real fermions. The additional degrees of freedom, neglected in the renormalization-group theory, lead to a new phase…
We consider nonequilibrium critical dynamics of the two-dimensional Ising model for which the initial state is prepared by switching on random fields with zero mean and variance $H$. In the initial state there is no magnetic order but the…
We study a model of two-dimensional interacting monomers which has two symmetric absorbing states and exhibits two kinds of phase transition; one is an order-disorder transition and the other is an absorbing phase transition. Our focus is…
Epstein's model for a civil disorder is an agent-based model that simulates a social protest process where the central authority uses the police force to dissuade it. The interactions of police officers and citizens produce dynamics that do…
Activated transitions have rates that are often exponentially small in system size. Extracting the associated activation barriers is challenging in practice, especially in the deeply metastable regimes and in the presence of disorder. Here,…
In this paper we study the phase diagram of two Ising planes coupled by a standard spin-spin interaction with bond randomness in each plane. The whole phase diagram is analyzed by help of Monte Carlo simulations and field theory arguments.
This paper introduces and analyses a general statistical model, termed the RARE model, of random relaxation processes in disordered systems. The model considers excitations, that are randomly scattered around a reaction center in a general…
The theory of phase transitions is based on the consideration of "idealized" models, such as the Ising model: a system of magnetic moments living on a cubic lattice and having only two accessible states. For simplicity the interaction is…
We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality…
An alternative model for a description of magnetization processes in coupled 2D spin-electron systems has been introduced and rigorously examined using the generalized decoration-iteration transformation and the corner transfer matrix…
We examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials which do not diverge at the origin, are free of attractive parts and decay fast enough to zero as the interparticle…
This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions interactions arise naturally in several…
In this paper we consider an approach, which allows researching a processes of order-disorder transition in various systems (with any distribution of the exchange integrals signs) in the frame of Ising model. A new order parameters, which…
Thermal quenching has been used to find metastable materials such as hard steels and metallic glasses. More recently, quenching-based phase control has been applied to correlated electron systems that exhibit metal--insulator, magnetic or…
We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical…
We investigate the stochastic resonance phenomena in the field-driven Ising model on small-world networks. The response of the magnetization to an oscillating magnetic field is examined by means of Monte Carlo dynamic simulations, with the…
We introduce a one dimensional disordered Ising model which at zero temperature is characterized by a non-trivial, non-self-averaging, overlap probability distribution when the impurity concentration vanishes in the thermodynamic limit. The…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…
We consider the 2D $J_1-J_2$ classical XY model on a square lattice. In the frustrated phase corresponding to $J_2>J_1/2$, an Ising order parameter emerges by an ``order due to disorder'' effect. This leads to a discrete symmetry plus the…