No abstract

We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff's idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) XY and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, ξ ∝ exp(c/ T /TKT − 1), we determine the KT transition temperature and the decay exponent η as TKT = 0.8933(6) and η = 0.243(5) for the 2D XY model. We investigate two transitions of the KT type for the 2D q-state clock models with q = 6, 8, 12, and for the first time confirm the prediction of η = 4/q 2 at T1, the low-temperature critical point between the ordered and XY-like phases, systematically.

Recently, Wang and Landau proposed a new random walk algorithm that can be very efficiently applied to many problems. Subsequently, there has been numerous studies on the algorithm itself and many proposals for improvements were put forward. However, fundamental questions such as what determines the rate of convergence has not been answered. To understand the mechanism behind the Wang-Landau method, we did an error analysis and found that a steady state is reached where the fluctuations in the accumulated energy histogram saturate at values proportional to [log(f )] −1/2 . This value is closely related to the error corrections to the Wang-Landau method. We also study the rate of convergence using different "tuning" parameters in the algorithm.

We study the two-dimensional classical XY model by the large-scale Monte Carlo simulation of the Swendsen-Wang multi-cluster algorithm using multiple GPUs on the open science supercomputer TSUBAME 2.0. Simulating systems up to the linear system size L = 65536, we investigate the Kosterlitz-Thouless (KT) transition. Using the generalized version of the probability-changing cluster algorithm based on the helicity modulus, we locate the KT transition temperature in a self-adapted way. The obtained inverse KT temperature β KT is 1.11996(6). We estimate the exponent to specify the multiplicative logarithmic correction, −2r, and precisely reproduce the theoretical prediction −2r = 1/8.

No abstract