Explicit Renormalization Group for D=2 random bond Ising model with long-range correlated disorder

TL;DR

This paper studies the effects of long-range correlated disorder on the two-dimensional random bond Ising model using an explicit fermionic renormalization group approach, revealing a new fixed point and calculating critical exponents.

Contribution

It introduces an explicit fermionic RG method to analyze long-range disorder effects, identifying a new fixed point and computing associated critical exponents.

Findings

Discovery of a new fixed point due to long-range correlated disorder.

Calculation of correlation length exponent at the new fixed point.

Agreement of results with the extended Harris criterion.

Abstract

We investigate the explicit renormalization group for fermionic field theoretic representation of two-dimensional random bond Ising model with long-range correlated disorder. We show that a new fixed point appears by introducing a long-range correlated disorder. Such as the one has been observed in previous works for the bosonic ($\phi^4$) description. We have calculated the correlation length exponent and the anomalous scaling dimension of fermionic fields at this fixed point. Our results are in agreement with the extended Harris criterion derived by Weinrib and Halperin.