Phase transitions in one-dimensional Riesz gases with long-range interaction

TL;DR

This paper provides numerical evidence for phase transitions in one-dimensional Riesz gases with long-range interactions, identifying fluid, quasisolid, and solid phases depending on temperature and interaction parameter s.

Contribution

It introduces the first numerical study of phase transitions in 1D Riesz gases with non-singular interactions, revealing a phase diagram with multiple transitions.

Findings

Existence of two distinct phase transitions depending on temperature and s.

Identification of a fluid to quasisolid transition similar to BKT transition.

Observation of a freezing transition leading to a solid phase.

Abstract

We provide numerical evidence for the existence of phase transitions with respect to the temperature in the one-dimensional Riesz gases with non-singular pair interaction, that is particles on the line interacting via the potential $-|r|^{-s}$, where $s \in (-1, 0)$. Our numerics hint for the existence of two distinct phase transitions whose critical temperatures depend on $s$, namely a first transition which separates between a fluid and a quasisolid phase reminiscent of the Berezinski-Kosterlitz-Thouless (BKT) transition, and a second transition below which freezing occurs and the system is in a solid phase. We determine the phase diagram with respect to $s$ and the temperature $T$, which we find to be consistent with the known (or expected) results on the 1D Coulomb gas ($s = -1$), known to be a solid at all temperature, and the Dyson log--gas ($s = 0$) which exhibits a BKT transition at $T = 1/2$ and which is believed to be a fluid at all positive temperature.