RG and logarithmic CFT multicritical properties of randomly diluted Ising models

TL;DR

This paper explores multicritical behaviors in disordered Ising models using RG and conformal field theory, focusing on logarithmic CFT aspects and generalizations of universality classes near critical dimensions.

Contribution

It introduces generalized universality classes for disordered Ising models and bridges RG and CFT approaches, especially in the context of logarithmic conformal field theories.

Findings

Identification of multicritical points in disordered Ising models.

Development of RG and CFT methods for analyzing these multicritical behaviors.

Insights into logarithmic CFT quantities relevant for disordered systems.

Abstract

We discuss how a spin system, which is subject to quenched disorder, might exhibit multicritical behaviors at criticality if the distribution of the impurities is arbitrary. In order to provide realistic candidates for such multicritical behaviors, we discuss several generalizations of the standard randomly diluted Ising's universality class adopting the $\epsilon$-expansion close to several upper critical dimensions. In the presentation, we spend a special effort in bridging between CFT and RG results and discuss in detail the computation of quantities, which are of prominent interest in the case of logarithmic CFT.