Critical behavior of the specific heat in the two dimensional site diluted Ising system

Logarithmic corrections to gap scaling in random-bond Ising strips

“…The present results contribute, albeit indirectly, to the growing body of evidence favouring strong universality (that is, pure-system behaviour with logarithmic corrections) in the two-dimensional random Ising model [1,2,3,4]. This is to be contrasted to recent work [6,7], according to which critical indices would vary with disorder, but so as to keep the ratio γ/ν constant at the pure system's value (the so-called weak universality scenario [8]). …”

“…Recent numerical work claiming weak universality to hold [6,7] does not address the issue either, though it is easy to see that the procedures used in those calculations pick out averaged correlations, as they rely respectively on variants of the fluctuationdissipation theorem [6] or on explicit averaging [7].…”

“…Early proposals of drastic alterations in the values of critical indices [5] have thus been essentially discarded. However, recent results [6,7] have appeared, according to which critical indices would vary with disorder, but so as to keep the ratio γ/ν constant at the pure system's value (the so-called weak universality scenario [8]). In order to solve this controversy, it is important to undertake independent tests of several aspects of the problem.…”

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

“…[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. [29,30,31,32,33]).…”

Specific heat of two-dimensional diluted magnets

“…[11,12] On the other hand, simulations on the two-dimensional site-diluted Ising model seemed to indicate that the critical peak in C, present at weak dilution, disappears at moderate dilution, well below the percolation threshold [13], with a broad maximum above the critical temperature. [14][15][16][17][18] Certainly, a finite value of the specific heat at T c would invalidate (1). However, recent Monte Carlo work [19] suggests that the field-theoretical results may be correct also in the case of moderate site-dilution.…”