HIGH-PRECISION MONTE-CARLO STUDY OF THE 2-DIMENSIONAL XY VILLAIN MODEL

We report two sets of high-precision Monte Carlo simulations of the two-dimensional XY model in Villain's formulation on large square lattices, employing the single-cluster update algorithm. In one set of simulations we use improved estimators to study the correlation length xi and susceptibility chi in the high-temperature phase. On a 1200 X 1200 lattice this allows measurements up to xi almost-equal-to 140 with statistical errors less than 0.25%. We judge quantitatively the advantage of using improved estimators, estimate autocorrelation times, and compare the numerical efficiency of various definitions of the correlation length. From least-square fits to these data we find clear support for the exponential divergence predicted by Kosterlitz and Thouless. The other set of simulations is performed in the vicinity of the transition point. Here we apply finite-size-scaling theory to obtain an estimate for the exponent eta at criticality.