Determination of the critical parameter with system size in a 2D classical XY-model

The first-order transition in the classical two-dimensional (2D) XY-model with the modified nearest neighbor interaction potential is investigated in computer simulations using Boltzmann's microcanonical ensemble. We use the property of negative specific-heat, of a finite-isolated system, to determine the critical value of the parameter q (qc) above which the transition is first-order. We have studied the variation of qc with system size. It has been found that qc increases with the system size, when the later is small.