Counterions at Charged Cylinders: Criticality and universality beyond mean-field

TL;DR

This paper investigates the counterion-condensation transition at charged cylinders using Monte Carlo simulations, revealing critical behavior and universality beyond mean-field theory in both 2D and 3D.

Contribution

It introduces a combined finite-size and finite-ion-number analysis to determine critical behavior and confirms universality of critical exponents beyond mean-field theory.

Findings

Critical exponents agree with mean-field predictions in 2D and 3D.

Universal jump in heat capacity at the transition in 3D.

Discrete peaks in heat capacity in 2D indicating successive counterion condensation.

Abstract

The counterion-condensation transition at charged cylinders is studied using Monte-Carlo simulation methods. Employing logarithmically rescaled radial coordinates, large system sizes are tractable and the critical behavior is determined by a combined finite-size and finite-ion-number analysis. Critical counterion localization exponents are introduced and found to be in accord with mean-field theory both in 2 and 3 dimensions. In 3D the heat capacity shows a universal jump at the transition, while in 2D, it consists of discrete peaks where single counterions successively condense.