Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses

Abstract

From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scheme involving a set of scaling formulas which expresses to leading order the temperature (T) and the system size (L) dependences of thermodynamic observables over a much wider range of T than the corresponding one in the conventional scaling scheme. The extended scaling, illustrated by data on the canonical 2d ferromagnet and on the 3d bimodal Ising spin glass, leads to consistency in the estimates of critical parameters obtained from scaling analyses for different observables.

Critical behavior of three-dimensional Ising spin glass models

“…As already noted in Ref. 29, this scheme shows an apparent improvement of the scaling behavior with respect to the naive approach in which scaling corrections are simply neglected, at least for some quantities, e.g., the overlap susceptibility. However, as we shall show, such an improvement is only marginal for the purpose of obtaining accurate results.…”

“…24, the approximate expression proposed in Ref. 29 has the correct qualitative shape, but differs significantly from the quantitative point of view. For these reasons, we do not expect the scaling Ansatz (88) to be particularly useful to estimate η from our data.…”

“…Eq. (29). Since R ξ is not exactly equal to R * ξ , we must take into account the O(L −1/ν ) corrections.…”

“…It consists in a particular choice of scaling variables, which, according to Ref. 29, should somehow decrease scaling corrections and thus allow a faster convergence to the critical limit. Let us consider first ξ/L.…”

“…to belong to a universality class which is independent of the details of the model and, in particular, of the disorder distribution. Several numerical works 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33 have addressed these issues, considering various Ising spin-glass models, characterized by different disorder distributions, with or without dilution. Over the years many estimates of the critical exponents have been obtained.…”