Finite size effects on the phase diagram of the thermodynamical cluster model

TL;DR

This paper investigates how finite size and Coulomb effects alter the phase diagram of the thermodynamical cluster model, revealing persistent ensemble inequivalence and modified phase transition features.

Contribution

It demonstrates the impact of finite size and Coulomb interactions on the phase diagram and ensemble properties of the model, extending understanding beyond the idealized infinite, uncharged case.

Findings

Finite size reproduces thermodynamic anomalies of phase transitions.

Coulomb effects significantly modify the phase diagram.

Ensemble inequivalence persists with Coulomb interactions.

Abstract

The thermodynamical cluster model is known to present a first-order liquid-gas phase transition in the idealized case of an uncharged, infinitely extended medium. However, in most practical applications of this model, the system is finite and charged. In this paper we study how the phase diagram is modified by finite size and Coulomb effects. We show that the thermodynamic anomalies which are associated to the finite system counterpart of first order phase transitions, are correctly reproduced by this effective model. However, approximations in the calculation of the grandcanonical partition sum prevent obtaining the exact mapping between statistical ensembles which should be associated to finite systems. The ensemble inequivalence associated to the transition persists in the presence of Coulomb, but the phase diagram is deeply modified with respect to the simple liquid-gas phase transition characteristic of the neutral system.