Counterions at Charged Cylinders: Criticality and universality beyond   mean-field
  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. 
Ali Naji and Roland R. Netz