Counter-ion condensation and Kosterlitz-Thouless transition

The similarity between counter-ion condensations in polyelectrolyte rod systems and Kosterlitz-Thouless phase transitions in two-dimensional systems is discussed at the level of mean-field theory. Based on the similarity, the renormalization group theory is applied to polyelectrolyte liquid systems aligned in parallel. It is found that the critical separation between monovalent charges for the counter-ion condensation is renormalized in polyelectrolyte liquid systems and becomes shorter than the Bjerrum length which is the critical separation predicted by the mean-field theory for a dilute solution of polyelectrolyte rods