Equidistant versus bipartite ground states for 1D classical fluids at fixed particle density

TL;DR

This paper investigates the phase transition between equidistant and bipartite ground states in one-dimensional classical fluids with long-range interactions, revealing universal mean-field critical behavior and non-universal phenomena with a hard-core.

Contribution

It provides a detailed analysis of the phase transition and critical phenomena in 1D classical fluids, including the Lennard-Jones model, and identifies the tricritical point and the effects of a hard-core.

Findings

Equidistant chain dominates for small spacing A

A second-order phase transition occurs at critical A=A_c

Hard-core inclusion leads to non-universal critical exponents

Abstract

We study the ground-state properties of one-dimensional fluids of classical (i.e., non-quantum) particles interacting pairwisely via a potential, at the fixed particle density $\rho$. Restricting ourselves to periodic configurations of particles, two possibilities are considered: an equidistant chain of particles with the uniform spacing $A=1/\rho$ and its simplest non-Bravais modulation, namely a bipartite lattice composed of two equidistant chains, shifted with respect to one another. Assuming the long range of the interaction potential, the equidistant chain dominates if $A$ is small enough, $0<A<A_c$. At a critical value of $A=A_c$, the system undergoes a continuous second-order phase transition from the equidistant chain to a bipartite lattice. The energy and the order parameter are singular functions of the deviation from the critical point $A-A_c$ with universal (i.e., independent of the model's parameters) mean-field values of critical exponents. The tricritical point at which the curve of continuous second-order transitions meets with the one of discontinuous first-order transitions is determined. The general theory is applied to the Lennard-Jones model with the $(n,m)$ Mie potential for which the phase diagram is constructed. The inclusion of a hard-core around each particle reveals a non-universal critical phenomenon with an $m$-dependent critical exponent.