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Phase diagram and pattern formation in two-dimensional Ising model with coupling between order parameter and lattice vibrations is investigated by Monte-Carlo simulations. It is shown that if the coupling is strong enough (or phonons are…
In a variety of systems which exhibit aging, the two-time response function scales as $R(t,s)\approx s^{-1-a} f(t/s)$. We argue that dynamical scaling can be extended towards conformal invariance, obtaining thus the explicit form of the…
We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links $a$ can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in…
The dynamics of non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The…
Using extensive Monte Carlo simulations we study aging properties of two disordered systems quenched below their critical point, namely the two-dimensional random-bond Ising model and the three-dimensional Edwards-Anderson Ising spin glass…
The phase-ordering kinetics of the ferromagnetic two-dimensional Ising model with uniform bond disorder is investigated by intensive Monte Carlo simulations. Simple ageing behaviour is observed in the single-time correlator and the two-time…
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…
Local scale invariance (LSI) has been recently proposed as a possible extension of the dynamical scaling in systems at the critical point and during phase ordering. LSI has been applied inter alia to provide predictions for the scaling…
Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme…
We study numerically the phase-ordering kinetics of the two-dimensional site-diluted Ising model. The data can be interpreted in a framework motivated by renormalization-group concepts. Apart from the usual fixed point of the non-diluted…
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster method and is much more efficient than the…
Spin correlation functions (up to the 3-site one) of disordered Ising model with the nearest neighbour interaction are calculated and investigated within a two-site cluster approximation for both quenched and annealed cases. The approach…
The aspects of phase transitions in the two-dimensional Ising models modified by quenched and annealed site disorder are discussed in the framework of fermionic approach based on the reformulation of the problem in terms of integrals with…
Large-scale Monte Carlo simulations are used to explore the effect of quenched disorder on one dimensional, non-equilibrium kinetic Ising models with locally broken spin symmetry, at zero temperature (the symmetry is broken through…
In spin systems such as the Ising model, the local order and disorder can be characterized by the order-parameter and energy density profiles $\langle \sigma ({\bf r}_1) \rangle$ and $\langle \epsilon ({\bf r}_2) \rangle$, respectively.…
We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard…
Until very recently, the asymptotic occurrence of intrinsic anomalous scaling has been expected to require concomitant effects for kinetically rough interfaces, like quenched disorder or morphological instabilities. However, counterexamples…
We investigate a disordered multi-dimensional linear system in which the interaction parameters vary stochastically in time with defined temporal correlations. We refer to this type of disorder as "annealed", in contrast to quenched…
We study numerically the phase-ordering kinetics of the site-diluted and bond-diluted Ising models after a quench from an infinite to a low temperature. We show that the speed of growth of the ordered domain's size is non-monotonous with…
We study numerically the aging dynamics of the two-dimensional p-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior…