Universal dependence on disorder of two-dimensional randomly diluted and random-bond±JIsing models

Abstract

We consider the two-dimensional randomly site diluted Ising model and the random-bond ±J Ising model (also called Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of thermodynamic quantities can be derived from a set of renormalization-group equations, in which disorder is a marginally irrelevant perturbation at the two-dimensional Ising fixed point. We discuss their solutions, focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder.Then, we present a finite-size scaling analysis of high-statistics Monte Carlo simulations. The numerical results confirm the renormalization-group predictions, and in particular the universality of the logarithmic corrections to the Ising behavior due to quenched dilution.

Scaling analysis of the site-diluted Ising model in two dimensions

“…Indeed, plots of the measured specific heat as a function of the double logarithm of the lattice extent are contained in Refs. [15,18] and Refs. [18,19,20] for the RBIM and the RSIM, respectively.…”

“…[15,18] and Refs. [18,19,20] for the RBIM and the RSIM, respectively. However, in [28] it was claimed that such apparent double-logarithmic FSS behaviour does not necessarily imply [29] [30] and theoretical support for finite C ∞ (t) [31,32] [33] or numerical support for finite C ∞ (t) [28,34] [ 35,36,37,38] divergence of the specific heat, and numerically based counter-claims that the specific heat remains finite (so that α < 0 or α = 0 andα < 0) in the random-bond [28,34] and random-site models [35,36,37,38] also exist (see also Refs.…”

“…(2.12), are found in Refs. [15,16,17,18] and Refs. [18,19,20] for the bond-disordered and random-site Ising models, respectively (see also Refs.…”

“…[15,16,17,18] and Refs. [18,19,20] for the bond-disordered and random-site Ising models, respectively (see also Refs. [12,14,21,22,23,24,25,26,27]).…”

“…[6],â 2 is related to the specific-heat correction exponentα appearing in (2.1) viâ 18) having used the established value (2.9) for the leading gap exponent [3]. The elusive specific heat scaling exponents α,α can thus be measured from the density (2.7) together with (2.10) and (2.18) and, in this way, one can distinguish between the competing α = 0, α = 0 and α < 0 orα < 0 scenarios.…”