Phenomenological theory of the Potts model evaporation-condensation transition

Abstract

We present a phenomenological theory describing the finite-size evaporationcondensation transition of the q-state Potts model in the microcanonical ensemble. Our arguments rely on the existence of an exponent σ, relating the surface and the volume of the condensed phase droplet. The evaporation-condensation transition temperature and energy converge to their infinite-size values with the same power, a = (1 − σ)/(2 − σ), of the inverse of the system size. For the 2D Potts model we show, by means of efficient simulations up to q = 24 and 1024 2 sites, that the exponent a is compatible with 1/4, in disagreement with previous studies. While this value cannot be addressed by the evaporation-condensation theory developed for the Ising model, it is obtained in the present scheme if σ = 2/3, in agreement with previous theoretical guesses. The connection with the phenomenon of metastability in the canonical ensemble is also discussed. p-6