Exploiting a semi-analytic approach to study first order phase transitions

TL;DR

This paper extends a semi-analytic method for studying first order phase transitions, demonstrating its applicability beyond low temperatures and to athermal systems, with validation on various models and analytical examples.

Contribution

The authors generalize a semi-analytic approach to analyze first order phase transitions, showing it works for stronger transitions and athermal problems, broadening its applicability.

Findings

Method accurately locates coexistence lines.

Thermodynamic quantities like entropy and energy are derived from the method.

Validated on Potts, Bell-Lavis, and lattice gas models.

Abstract

In a previous contribution, Phys. Rev. Lett 107, 230601 (2011), we have proposed a method to treat first order phase transitions at low temperatures. It describes arbitrary order parameter through an analytical expression $W$, which depends on few coefficients. Such coefficients can be calculated by simulating relatively small systems, hence with a low computational cost. The method determines the precise location of coexistence lines and arbitrary response functions (from proper derivatives of $W$). Here we exploit and extend the approach, discussing a more general condition for its validity. We show that in fact it works beyond the low $T$ limit, provided the first order phase transition is strong enough. Thus, $W$ can be used even to study athermal problems, as exemplified for a hard-core lattice gas. We furthermore demonstrate that other relevant thermodynamic quantities, as entropy and energy, are also obtained from $W$. To clarify some important mathematical features of the method, we analyze in details an analytically solvable problem. Finally, we discuss different representative models, namely, Potts, Bell-Lavis, and associating gas-lattice, illustrating the procedure broad applicability.