Superfluid Transition and Specific Heat of the 2D <i>x</i>-<i>y</i> Model: Monte Carlo Simulation

Abstract

We present results of large-scale Monte Carlo simulations of the 2D classical x-y model on the square lattice. We obtain high accuracy results for the superfluid fraction and for the specific heat as a function of temperature, for systems of size L×L with L up to 212. Our estimate for the superfluid transition temperature is consistent with those furnished in all previous studies. The specific heat displays a well-defined peak, whose shape and position are independent of the size of the lattice for L>28, within the statistical uncertainties of our calculations. The implications of these results on the interpretation of experiments on adsorbed thin films of 4He are discussed.

Keywords

• phase transitions
• specific heat
• Monte Carlo simulation
• worm algorithm
• superfluidity
• <i>x</i>-<i>y</i> model