Thermodynamics of two-component log-gases with alternating charges

TL;DR

This paper derives the exact thermodynamics of a one-dimensional alternating charge log-gas using the Thermodynamic Bethe ansatz, extending previous results for unrestricted charges and analyzing behavior near collapse and with hard-core interactions.

Contribution

It provides the first exact thermodynamic analysis of an ordered alternating charge log-gas on a line, expanding on prior work with unrestricted charges.

Findings

Exact grand partition function for ordered log-gas obtained

Thermodynamics verified via small-β expansion and collapse analysis

Inclusion of hard core extends analysis beyond collapse point

Abstract

We consider a one-dimensional gas of positive and negative unit charges interacting via a logarithmic potential, which is in thermal equilibrium at the (dimensionless) inverse temperature $\beta$. In a previous paper [Samaj, L.: J. Stat. Phys. 105, 173-191 (2001)], the exact thermodynamics of the unrestricted log-gas of pointlike charges was obtained using an equivalence with a (1+1)-dimensional boundary sine-Gordon model. The present aim is to extend the exact study of the thermodynamics to the log-gas on a line with alternating $\pm$ charges. The formula for the ordered grand partition function is obtained by using the exact results of the Thermodynamic Bethe ansatz. The complete thermodynamics of the ordered log-gas with pointlike charges is checked by a small-$\beta$ expansion and at the collapse point $\beta_c=1$. The inclusion of a small hard core around particles permits us to go beyond the collapse point. The differences between the unconstrained and ordered versions of the log-gas are pointed out.