Eur. Phys. J. E (2017) 40: 70
https://doi.org/10.1140/epje/i2017-11559-7

Regular Article

Scaling and criticality of the Manning transition

¹ Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, 34141, Deajeon, Korea
² Department of Physics, Pusan National University, 46241, Busan, Korea

^* e-mail: y.w.kim@kaist.ac.kr

Received: 31 May 2017
Accepted: 20 July 2017
Published online: 3 August 2017

Abstract

We consider a system consisting of a charged cylinder in the presence of neutralizing counterions. This system is well known to exhibit the Manning transition of counterion condensation onto the charged cylinder. We study the criticality and the scaling properties of the Manning transition, analyzing involved thermodynamic quantities such as condensed fraction, its fluctuation, and heat capacity. Through the Monte Carlo simulations and finite-size scaling analysis, we find that near the transition point the examined quantities exhibit scale-invariant behaviors with specific exponents, which provides an evidence that the Manning transition is a critical phenomenon having a scale-invariant property, analogous to bulk phase transitions. Furthermore, we numerically confirm that such scaling properties are not affected by the coupling strength.