Nonlinear susceptibilities of a weakly-disordered uniaxial ferromagnet in the critical region

TL;DR

This paper calculates nonlinear susceptibilities and effective coupling constants for a three-dimensional random Ising model at criticality, revealing significant differences from pure magnets that can help identify random critical behavior.

Contribution

It provides the first detailed calculation of v_6, chi_4, and chi_6 for the random Ising model at criticality, highlighting their differences from pure systems.

Findings

v_6/v_4^2 ratio is 0.87 for random vs. 1.65 for pure magnets

Universal susceptibility ratios differ by factors of 1.6 and 2.7 between random and pure models

Differences in these quantities can be used to experimentally identify random critical behavior

Abstract

For the three-dimensional random Ising model, the effective sextic coupling constant v_6 and the nonlinear susceptibilities of the fourth (chi_4) and sixth (chi_6) orders are calculated at criticality. These quantities are shown to differ markedly from their counterparts for pure uniaxial magnets. In particular, the ratio v_6/v_{4}^2 entering the equation of state of the random Ising model turns out to be equal to 0.87, while in pure magnets v_6/v_{4}^2 = 1.65. The universal susceptibility ratios m^3 chi_4/chi^2 and m^6 chi_6/chi^3 (m - the inverse correlation length) are found to differ by factors 1.6 and 2.7, respectively, for random and uniform Ising models. These big differences of the universal quantities can be measured both in physical and computer experiments, and such measurements may be considered as a tool for an identification of the random critical behavior.