RENORMALIZATION GROUP SOLUTION FOR THE TWO-DIMENSIONAL RANDOM BOND POTTS MODEL WITH BROKEN REPLICA SYMMETRY

TL;DR

This paper presents a new renormalization group solution for the 2D random bond Potts model, highlighting the role of broken replica symmetry in reaching a universal behavior distinct from the replica symmetric case.

Contribution

It introduces a novel RG solution demonstrating how broken replica symmetry leads to a different universality class in the 2D random bond Potts model.

Findings

Universality class depends on initial replica symmetry state.

Broken replica symmetry results in a new fixed point.

Model exhibits universality with broken replica symmetry.

Abstract

We find a new solution of the renormalization group for the Potts model with ferromagnetic random valued coupling constants. The solution exhibits universality and broken replica symmetry. It is argued that the model reaches this universality class if the replica symmetry is broken initially. Otherwise the model stays with the replica symmetric renormalization group flow and reaches the fixed point which has been considered before.