Randomly coupled minimal models

TL;DR

This paper uses 1-loop renormalisation group equations to study how randomness affects multi-critical minimal conformal models, revealing that coupled models flow to decoupled models with lower criticality.

Contribution

It demonstrates that randomly coupled minimal models flow to decoupled models with reduced criticality, extending previous results to multiple coupled models.

Findings

Two coupled models flow to two decoupled models with lower criticality

Extension to M models shows similar decoupling behavior

Results provide insight into the effect of randomness on conformal models

Abstract

Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled $M_p$ models and found that they flow in two decoupled $M_{p-1}$ models, in the infra-red limit. This result is then extend to the case with $M$ randomly coupled $M_p$ models, which will flow toward $M$ decoupled $M_{p-1}$.