MONTE-CARLO STUDY OF THE PLANAR SPIN MODEL

We have simulated the two-dimensional classical planar spin model using the Metropolis Monte Carlo technique. The loss of long-range order as a function of the size of the lattice was confirmed. The energy and specific heat were calculated for a square lattice of 900, 3 600, and 10 000 spins. A sharp specific-heat peak was found at kBTJ=1.02 J is the nearest-neighbor coupling), 15% above the transition temperature kBTcJ=0.89. Tc was determined by fitting the spin-spin correlation function and the susceptibility to the forms of the Kosterlitz-Thouless theory. The density of vortex pairs was computed and found to increase exponentially with inverse temperature. At Tc vortex pairs begin to unbind and also larger clusters of vortices appear and unbind as the temperature is increased. These larger clusters may be responsible for the specific-heat peak being sharper and closer to Tc than simple theories predict. © 1979 The American Physical Society.