Random Bond Potts Model: the Test of the Replica Symmetry Breaking

TL;DR

This paper computes the averaged spin-spin correlation function squared in the random bond Potts model using renormalization group and conformal field theory, aiming to distinguish between replica symmetric and broken fixed points.

Contribution

It provides a fixed point calculation for the correlation function squared in the random bond Potts model, incorporating both replica symmetric and symmetry broken scenarios.

Findings

Results enable numerical tests to distinguish critical behaviors.

Calculations performed for both replica symmetric and broken fixed points.

Uses epsilon-expansion near the Ising model limit.

Abstract

Averaged spin-spin correlation function squared $\overline{<\sigma(0)\sigma(R)>^{2}}$ is calculated for the ferromagnetic random bond Potts model. The technique being used is the renormalization group plus conformal field theory. The results are of the $\epsilon$ - expansion type fixed point calculation, $\epsilon$ being the deviation of the central charge (or the number of components) of the Potts model from the Ising model value. Calculations are done both for the replica symmetric and the replica symmetry broken fixed points. The results obtained allow for the numerical simulation tests to decide between the two different criticalities of the random bond Potts model.