Critical exponents of the diluted Ising model between dimensions 2 and 4

TL;DR

This paper uses advanced field theoretical methods to calculate critical exponents of the diluted Ising model across dimensions 2 to 4, providing insights into phase transition behavior in disordered systems.

Contribution

It derives three-loop beta- and gamma-functions for the anisotropic mn-vector model and estimates critical exponents for the weakly diluted Ising model in various dimensions.

Findings

Critical exponents are calculated for 2 ≤ d < 4.

Resummation techniques' effectiveness is evaluated.

Estimates for the marginal order parameter component number m_c are provided.

Abstract

Within the massive field theoretical renormalization group approach the expressions for the beta- and gamma-functions of the anisotropic mn-vector model are obtained for general space dimension d in three-loop approximation. Resumming corresponding asymptotic series, critical exponents for the case of the weakly diluted quenched Ising model (m=1, n=0), as well as estimates for the marginal order parameter component number m_c of the weakly diluted quenched m-vector model are calculated as functions of d in the region 2 =< d <4. Conclusions concerning the effectiveness of different resummation techniques are drawn.