Correlation functions, free energies, and magnetizations in the two-dimensional random-field Ising model

Abstract

Transfer-matrix methods are used to calculate spin-spin correlation functions (G), Helmholtz free energies (f ) and magnetizations (m) in the two-dimensional random-field Ising model close to the zero-field bulk critical temperature Tc 0, on long strips of width L = 3 − 18 sites, for binary field distributions. Analysis of the probability distributions of G for varying spin-spin distances R shows that describing the decay of their averaged values by effective correlation lengths is a valid procedure only for not very large R. Connections between field-and correlation function distributions at high temperatures are established, yielding approximate analytical expressions for the latter, which are used for computation of the corresponding structure factor. It is shown that, for fixed R/L, the fractional widths of correlation-function distributions saturate asymptotically with L −2.2 . Considering an added uniform applied field h, a connection between f (h), m(h), the Gibbs free energy g(m) and the distribution function for the uniform magnetization in zero uniform field, P0(m), is derived and first illustrated for pure systems, and then applied for non-zero random field. From finite-size scaling and crossover arguments, coupled with numerical data, it is found that the width of P0(m) varies against (non-vanishing, but small) random-field intensity H0 as H −3/7 0 .

Multicanonical Monte Carlo study and analysis of tails for the order-parameter distribution of the two-dimensional Ising model

“…Introduction [68.1.1.1] A quantity of central importance for finitesize scaling analysis of critical phenomena is the order parameter distribution [1,2]. [68.1.1.2] Despite many years of research there remain open questions even for the much studied case of the Ising universality class [3,4,5,6,7,8,9,10,11,12].…”

Spin activity correlations in driven disordered systems

“…Some studies of the correlations in question are also performed in terms of selforganized criticality indicating that the systems out of equilibrium will self-organize to a critical state [29,30]. The spatial avalanche correlation functions have been studied on systems with other dimensionality [31] and topology [32][33][34][35], followed by some recent findings reported on computing correlation functions between different avalanches [36]. Temporal correlations have been previously investigated for the adiabatic case of ZT NEQ RFIM as well as on other types of systems [37][38][39][40], for instance in neuronal avalanche occurrence [41], demonstrated as the power-law distributed waiting times between the successive avalanches as opposed to the exponential type of distributions found for the systems in which the temporal correlations are absent.…”