The spectrum of massive excitations of 3d 3-state Potts model and universality

TL;DR

This paper investigates the mass spectrum of the 3D 3-state Potts model near critical points, testing universality of mass ratios in second order and weakly first order phase transitions, with implications for broader universality conjectures.

Contribution

It provides the first comparison of mass ratios in the 3D 3-state Potts model with universality predictions near both second order and weakly first order transitions.

Findings

Mass ratios near the Ising critical point agree with universality predictions.

Determined a mass ratio near the first order transition to compare with SU(3) gauge theory.

Results support extending universality of mass ratios to weakly first order transitions.

Abstract

We consider the mass spectrum of the 3$d$ 3-state Potts model in the broken phase (a) near the second order Ising critical point in the temperature - magnetic field plane and (b) near the weakly first order transition point at zero magnetic field. In the case (a), we compare the mass spectrum with the prediction from universality of mass ratios in the 3$d$ Ising class; in the case (b), we determine a mass ratio to be compared with the corresponding one in the spectrum of screening masses of the (3+1)$d$ SU(3) pure gauge theory at finite temperature in the deconfined phase near the transition. The agreement in the comparison in the case (a) would represent a non-trivial test of validity of the conjecture of spectrum universality. A positive answer to the comparison in the case (b) would suggest the possibility to extend this conjecture to weakly first order phase transitions.