Phenomenological theory of the Potts model evaporation-condensation transition

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 $\sigma$, 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, $a=(1-\sigma)/(2-\sigma)$, 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 $\sigma=2/3$, in agreement with previous theoretical guesses. The connection with the phenomenon of metastability in the canonical ensemble is also discussed.