1106.3870 (Fabrizio Baroni)

The mechanism of phase transitions enlightened by an elementary
Z_2-symmetric classical spin model    [PDF]

Fabrizio Baroni

In this paper we present the most elementary model that we know with a first order $\mathbb{Z}_2$-symmetry breaking phase transition. It is a classical spin model with potential energy assuming only two values, which despite its dramatic simplicity reproduces all the characteristic features of a first order symmetry breaking phase transition. Its aim is not to reproduce anyway some physical systems, but to enlighten the mechanics at the deep origin of a phase transition of any system. We consider the model as elementary in this sense. Indeed, it reveals in the most evident way how the Boltzmann factor competes with the entropic factor in order to generate the phase transition by varying the temperature. The paper ends revisiting the solutions of the Ising model and the spherical model (Berlin-Kac) in the mean-field version which show the same picture of the model introduced in this paper, but extended to continuous phase transitions. A limit of this analysis is that all the three models here considered satisfies the strong constraint of having the potential expressible as a function of the magnetization, thus they belong to the class of infinite-range systems. Anyway, we hope that this study may be helpful in finding out the general sufficiency conditions under which a potential can entail a phase transition in a general physical system also in the finite-range case.

View original: http://arxiv.org/abs/1106.3870