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

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