Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$

TL;DR

This paper investigates the critical behavior of a diluted Ising model with long-range interactions in three dimensions, identifying a new universality class and calculating the correlation length exponent using advanced field-theoretic methods.

Contribution

It introduces a three-loop renormalization group analysis of the long-range disordered Ising model, providing new estimates of critical exponents for specific interaction ranges.

Findings

Identification of a new long-range random universality class.

Estimation of the correlation length critical exponent $ u$ for $d=3$.

Application of three-loop RG functions and resummation techniques.

Abstract

We analyse the critical properties of a weakly diluted (random) Ising model with the long-range interaction decaying with distance $x$ as $\sim x^{-d-\sigma}$ in a $d$-dimensional space. It is known to belong to a new long-range random universality class for certain values of the decay parameter $\sigma$. Exploiting the field-theoretic renormalization group approach within the minimal subtraction scheme, we compute the three-loop renormalization group functions. On their basis, with the help of asymptotic series resummation methods, we estimate the correlation length critical exponent $\nu$ characterising the new universality class for $d=3$ and for those values of $\sigma$ for which long-range interactions are relevant for the critical behaviour.