We study the condensation transition of counterions on a charged cylinder viaMonte Carlo simulations. Varying the cylinder radius systematically in relationto the system size, we find that all counterions are bound to the cylinder andthe heat capacity shows a drop at a finite Manning parameter. A finite-sizescaling analysis is carried out to confirm the criticality of the completecondensation transition, yielding the same critical exponents with the Manningtransition. We show that the existence of the complete condensation isessential to explain how the condensation nature alters from continuous todiscontinuous transition.
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