Broad histogram relation for the bond number and its applications.

We discuss Monte Carlo methods based on the cluster (graph) representation for spin models. We derive a rigorous broad histogram relation (BHR) for the bond number; a counterpart for the energy was derived by Oliveira previously. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed. We show the efficiency of the BHR for the bond number in calculating the density of states and other physical quantities.

[1]  Jian-Sheng Wang.  Is the broad histogram random walk dynamics correct? , 1999 .

[2]  T. Penna,et al.  A Comparison Between Broad Histogram and Multicanonical Methods , 2000, cond-mat/0002176.

[3]  D. Landau,et al.  Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.

[4]  Chiaki Yamaguchi,et al.  Combination of improved multibondic method and the Wang-Landau method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  T.J.P. Penna,et al.  Broad histogram Monte Carlo , 1998 .

[6]  Berg,et al.  New approach to spin-glass simulations. , 1992, Physical review letters.

[7]  Probability-Changing Cluster Algorithm: Study of Three-Dimensional Ising Model and Percolation Problem , 2002, cond-mat/0203454.

[8]  Janke,et al.  Multibondic cluster algorithm for Monte Carlo simulations of first-order phase transitions. , 1995, Physical review letters.

[9]  Kawashima,et al.  Dual Monte Carlo and cluster algorithms. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  K. Hukushima,et al.  Exchange Monte Carlo Method and Application to Spin Glass Simulations , 1995, cond-mat/9512035.

[11]  P. M. C. Oliveira.  Broad histogram: an overview , 2000, cond-mat/0003300.

[12]  Y Okabe,et al.  Probability-changing cluster algorithm for Potts models. , 2001, Physical review letters.

[13]  Ferdinando Gliozzi.  Simulation of Potts models with real q and no critical slowing down. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  G. Parisi,et al.  Simulated tempering: a new Monte Carlo scheme , 1992, hep-lat/9205018.

[15]  D. Landau,et al.  Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Jian-Sheng Wang,et al.  Flat histogram Monte Carlo method , 2000 .

[17]  H. Herrmann,et al.  Broad Histogram Method , 1996, cond-mat/9610041.

[18]  Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[19]  Paulo Murilo Castro de Oliveira.  Broad histogram relation is exact , 1998 .

[20]  C. Fortuin,et al.  On the random-cluster model: I. Introduction and relation to other models , 1972 .

[21]  Configuration space for random walk dynamics , 1998, cond-mat/9805165.

[22]  Lik Wee Lee,et al.  Monte Carlo algorithms based on the number of potential moves , 1999 .

[23]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[24]  Kandel,et al.  General cluster Monte Carlo dynamics. , 1991, Physical review. B, Condensed matter.

[25]  Wolff,et al.  Collective Monte Carlo updating for spin systems. , 1989, Physical review letters.

[26]  Beale.  Exact distribution of energies in the two-dimensional ising model. , 1996, Physical review letters.

[27]  Lee,et al.  New Monte Carlo algorithm: Entropic sampling. , 1993, Physical review letters.