Probability-Changing Cluster Algorithm for Potts Models

We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, $p = 1 - e^{- J/ k_BT}$, in the process of the Monte Carlo spin update. Since we approach the canonical ensemble asymptotically, we can use the finite-size scaling analysis for physical quantities near the critical point. Simulating the two-dimensional Potts models to demonstrate the validity of the algorithm, we have obtained the critical temperatures and critical exponents which are consistent with the exact values; the comparison has been made with the invaded cluster algorithm.Comment: 4 pages including 5 eps figures, RevTeX, to appear in Phys. Rev. Let

Universal Finite-Size-Scaling Functions

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions. Keywords: Universal Finite-Size-Scaling Function; Ising Model; Order-Parameter Probability Distribution Function.Comment: 8 pages, Figures are available at http://glimmung.phys.sci.osaka-u.ac.jp/kikuchi/preprints.html or they will be sent upon request by e-mai