Self-avoiding walk on a square lattice with correlated vacancies

Edwards-Wilkinson depinning transition in fractional Brownian motion background

There are various reports about the critical exponents associated with the depinning transition. In this study, we investigate how the disorder strength present in the support can account for this diversity. Specifically, we examine the depinning transition in the quenched Edwards-Wilkinson (QEW) model on a correlated square lattice, where the correlations are modeled using fractional Brownian motion (FBM) with a Hurst exponent of H.We identify a crossover time [Formula: see text] that separates the dynamics into two distinct regimes: for [Formula: see text], we observe the typical behavior of pinned surfaces, while for [Formula: see text], the behavior differs. We introduce a novel three-variable scaling function that governs the depinning transition for all considered H values. The associated critical exponents exhibit a continuous variation with H, displaying distinct behaviors for anti-correlated ([Formula: see text]) and correlated ([Formula: see text]) cases. The critical driving force decreases with increasing H, as the host medium becomes smoother for higher H values, facilitating fluid mobility. This fact causes the asymptotic velocity exponent [Formula: see text] to increase monotonically with H.

Invasion percolation in short-range and long-range disorder background

In the original invasion percolation model, a random number quantifies the role of necks, or generally the quality of pores, ignoring the structure of pores and impermeable regions (to which the invader cannot enter). In this paper, we investigate invasion percolation (IP), taking into account the impermeable regions, the configuration of which is modeled by ordinary and Ising-correlated site percolation (with short-range interactions, SRI), on top of which the IP dynamics is defined. We model the long-ranged correlations of pores by a random Coulomb potential (RCP). By examining various dynamical observables, we suggest that the critical exponents of Ising-correlated cases change considerably only in the vicinity of the critical point (critical temperature), while for the ordinary percolation case the exponents are robust against the occupancy parameter p. The properties of the model for the long-range interactions [LRI (RCP)] are completely different from the normal IP. In particular, the fractal dimension of the external frontier of the largest hole is nearly 4/3 for SRI far from the critical points, which is compatible with normal IP, while it converges to 1.099±0.04 for RCP. For the latter case, the time dependence of our observables is divided into three parts: the power law (short time), the logarithmic (moderate time), and the linear (long time) regimes. The second crossover time is shown to go to infinity in the thermodynamic limit, whereas the first crossover time is nearly unchanged, signaling the dominance of the logarithmic regime. The average gyration radius of the growing clusters, the length of their external perimeter, and the corresponding roughness are shown to be nearly constant for the long-time regime in the thermodynamic limit.

Superstatistical two-temperature Ising model

The previous approach of the nonequilibrium Ising model was based on the local temperature in which each site or part of the system has its own specific temperature. We introduce an approach of the two-temperature Ising model as a prototype of the superstatistic critical phenomena. The model is described by two temperatures (T_{1},T_{2}) in a zero magnetic field. To predict the phase diagram and numerically estimate the exponents, we develop the Metropolis and Swendsen-Wang Monte Carlo method. We observe that there is a nontrivial critical line, separating ordered and disordered phases. We propose an analytic equation for the critical line in the phase diagram. Our numerical estimation of the critical exponents illustrates that all points on the critical line belong to the ordinary Ising universality class.