General approach for studying first-order phase transitions at low temperatures

TL;DR

This paper introduces a versatile protocol combining analytic expressions, enhanced tempering simulations, and finite size analysis to study first-order phase transitions at low temperatures effectively.

Contribution

It presents a novel, general approach that integrates analytic and simulation techniques for analyzing discontinuous phase transitions at low temperatures.

Findings

Successfully applied to four models demonstrating phase coexistence detection.

Accurately locates coexistence lines and phase densities.

Efficiently estimates thermodynamic limits from finite size data.

Abstract

By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order parameters, whose coefficients are obtained from simple simulations. Once in such regimes simulations by standard algorithms are not reliable, an enhanced tempering method, the parallel tempering -- accurate for small and intermediate system sizes with rather low computational cost -- is used. Finally, from finite size analysis, one can obtain the thermodynamic limit. The procedure is illustrated for four distinct models, demonstrating its power, e.g., to locate coexistence lines and the phases density at the coexistence.