Effective critical behaviour of diluted Heisenberg-like magnets

TL;DR

This paper uses the field-theoretical renormalization group approach to explain the variation of effective critical exponents in diluted Heisenberg-like magnets, showing they depend on temperature distance from the critical point and match pure 3d Heisenberg exponents at criticality.

Contribution

It provides a theoretical explanation for the experimentally observed non-universal effective exponents in diluted Heisenberg magnets, aligning them with Harris criterion predictions.

Findings

Effective exponents vary with temperature distance from $T_c$

Exponents match pure 3d Heisenberg values at $T_c$

Theoretical model explains experimental observations

Abstract

In agreement with the Harris criterion, asymptotic critical exponents of three-dimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentration- and temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we use the field--theoretical renormalization group approach to explain this observation and to calculate the effective critical exponents of weakly diluted quenched Heisenberg-like magnet. Being non-universal, these exponents change with distance to the critical point $T_c$ as observed experimentally. In the asymptotic limit (at $T_c$) they equal to the critical exponents of the pure 3d Heisenberg magnet as predicted by the Harris criterion.