Configurational and energy landscape in one-dimensional Coulomb systems

TL;DR

This paper analyzes the energy landscape and configurations of a one-dimensional Coulomb system with charged colloids and counterions, revealing a cascade of phase transitions influenced by system size and pressure.

Contribution

It provides exact partition functions for fixed and variable colloid positions, uncovering the conditions for optimal counterion arrangements and symmetry breaking.

Findings

Identifies a cascade of phase transitions with system size in canonical ensemble.

Shows symmetry breaking in counterion distribution outside the confined segment.

Derives exact partition functions for different ensemble conditions.

Abstract

We study a one dimensional Coulomb system, where two charged colloids are neutralized by a collection of point counterions, with global neutrality. Temperature being given, two situations are addressed: the colloids are either kept at fixed positions (canonical ensemble), or the force acting on the colloids is fixed (isobaric-isothermal ensemble). The corresponding partition functions are worked out exactly, in view of determining which arrangement of counterions is optimal: how many counterions should be in the confined segment between the colloids? For the remaining ions outside, is there a left/right symmetry breakdown? We evidence a cascade of transitions, as system size is varied in the canonical treatment, or as pressure is increased in the isobaric formulation.