High-precision Monte Carlo study of the two-dimensional [ital XY] Villain model
- Institut fuer Theoretische Physik, Freie Universitaet Berlin, Arnimallee 14, D-1000 Berlin 33 (Germany) Hoechstleistungsrechenzentrum, Forschungszentrum Juelich, Postfach 1913, D-5170 Juelich (Germany)
- Institut fuer Theoretische Physik, Freie Universitaet Berlin, Arnimallee 14, D-1000 Berlin 33 (Germany)
We report two sets of high-precision Monte Carlo simulations of the two-dimensional [ital 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[times]1200 lattice this allows measurements up to [xi][approx]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.
- OSTI ID:
- 6022987
- Journal Information:
- Physical Review, B: Condensed Matter; (United States), Vol. 48:10; ISSN 0163-1829
- Country of Publication:
- United States
- Language:
- English
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SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTAL MODELS
CORRELATIONS
ALGORITHMS
COMPUTERIZED SIMULATION
KOSTERLITZ-THOULESS THEORY
MAGNETIC SUSCEPTIBILITY
MONTE CARLO METHOD
TWO-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
MAGNETIC PROPERTIES
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
PHYSICAL PROPERTIES
SIMULATION
665400* - Quantum Physics Aspects of Condensed Matter- (1992-)