Phenomenological theory of the Potts model evaporation-condensation transition

INFN-Gruppo Collegato di Parma - via G.P. Usberti, 7/A, 43124, Parma, Italy and Dipartimento di Fisica, Università di Roma “La Sapienza” - Piazzale Aldo Moro 5, 00185, Roma, Italy

Received: 3 December 2015
Accepted: 25 January 2016

Abstract

We present a phenomenological theory describing the finite-size evaporation-condensation 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, , of the inverse of the system size. For the 2D Potts model we show, by means of efficient simulations up to q = 24 and 1024² sites, that the exponent a is compatible with 1/4, assuming assymptotic finite-size convergence. While this value cannot be addressed by the evaporation-condensation theory developed for the Ising model, it is obtained in the present scheme if , in agreement with previous theoretical guesses. The connection with the phenomenon of metastability in the canonical ensemble is also discussed.