Crossover behavior in three-dimensional dilute spin systems

TL;DR

This paper investigates the crossover phenomena in three-dimensional dilute spin systems at high temperatures, focusing on universal scaling behaviors and crossover functions for magnetic susceptibility and correlation length.

Contribution

It provides a field-theoretical analysis of crossover functions and estimates universal ratios for dilute Ising, XY, and Heisenberg systems, advancing understanding of critical behavior.

Findings

Derived crossover functions for susceptibility and correlation length.

Estimated universal ratios of scaling-correction amplitudes.

Analyzed Gaussian-to-random and pure-Ising-to-random crossovers.

Abstract

We study the crossover behaviors that can be observed in the high-temperature phase of three-dimensional dilute spin systems, using a field-theoretical approach. In particular, for randomly dilute Ising systems we consider the Gaussian-to-random and the pure-Ising-to-random crossover, determining the corresponding crossover functions for the magnetic susceptibility and the correlation length. Moreover, for the physically interesting cases of dilute Ising, XY, and Heisenberg systems, we estimate several universal ratios of scaling-correction amplitudes entering the high-temperature Wegner expansion of the magnetic susceptibility, of the correlation length, and of the zero-momentum quartic couplings.