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In order to check on a recent suggestion that local scale invariance [M.Henkel et al. Phys.Rev.Lett. {\bf 87}, 265701 (2001)] might hold when the dynamics is of Gaussian nature, we have carried out the measurement of the response function…

The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…

Two-state spin systems is a classical topic in statistical physics. We consider the problem of computing the partition function of the systems on a bounded degree graph. Based on the self-avoiding tree, we prove the systems exhibits strong…

The phase transition kinetics of Ising gauge models are investigated. Despite the absence of a local order parameter, relevant topological excitations that control the ordering kinetics can be identified. Dynamical scaling holds in the…

Results are presented for a two-point correlation function of a spin-chain after a quantum quench for an intermediate time regime where inelastic effects are weak. A Callan-Symanzik like equation for the correlation function is explicitly…

The anisotropy parameter of two-dimensional equilibrium clusters of site percolation process in long-range self-affine correlated structures are studied numerically. We use a fractional Brownian Motion(FBM) statistic to produce both…

We study nonequilibrium dynamical properties of inhomogeneous systems, in particular at a free surface or at a defect plane. Thereby we consider nonconserved (model-A) dynamics of a system which is prepared in the high-temperature phase and…

We study the correlation function of the one-dimensional Ising model at fixed magnetization. Focusing on the scaling limit close to the zero-temperature fixed point, we show that this correlation function, in momentum space, exhibits…

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…

We comprehensively study non-equilibrium relaxation and aging processes in the two-dimensional random-site Ising model through numerical simulations. We discuss the dynamical correlation length as well as scaling functions of various…

The behaviour of the 3D axial next-nearest neighbour Ising (ANNNI) model at the uniaxial Lifshitz point is studied using Monte Carlo techniques. A new variant of the Wolff cluster algorithm permits the analysis of systems far larger than in…

The non-equilibrium dynamics of the kinetic spherical model, quenched to T<=T_c, with a non-conserved order-parameter is studied at its upper critical dimension d=d*=4. In the scaling limit where both the waiting time s and the observation…

Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling…

The classical regular and partial autocorrelation functions are powerful tools for stationary time series modelling and analysis. However, it is increasingly recognized that many time series are not stationary and the use of classical…

This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed,…

We study the influence of dissipation on the Ising-Gamma model. Through observables such as ground-state energy, order parameters, entanglement entropy, etc., we identify each phase region and provide the global phase diagram of the system.…

A new method for locating analytically critical temperatures is discussed. It is exact for selfdual systems. When applied the two coupled layers of Ising spins it deviates from our preliminary Monte Carlo estimates by 1.5 standard…

We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional…

The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…

At arbitrary temperature $T$, we solve for the dynamics of single molecule magnets composed of three classical Heisenberg spins either on a chain with two equal exchange constants $J_1$, or on an isosceles triangle with a third, different…