scholarly journals RELAXATION UNDER OUTFLOW DYNAMICS WITH RANDOM SEQUENTIAL UPDATING

2005 ◽  
Vol 16 (11) ◽  
pp. 1771-1783 ◽  
Author(s):  
SYLWIA KRUPA ◽  
KATARZYNA SZNAJD-WERON
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Square Lattice ◽  
One Dimensional ◽  
Sequential Updating ◽  
The Mean

In this paper we compare the relaxation in several versions of the Sznajd model (SM) with random sequential updating on the chain and square lattice. We start by reviewing briefly all proposed one-dimensional versions of SM. Next, we compare the results obtained from Monte Carlo simulations with the mean field results obtained by Slanina and Lavicka. Finally, we investigate the relaxation on the square lattice and compare two generalizations of SM, one suggested by Stauffer et al. and another by Galam. We show that there are no qualitative differences between these two approaches, although the relaxation within the Galam rule is faster than within the well known Stauffer et al. rule.

The Critical Behavior of the General Spin Blume–Capel Model

1998 ◽  
Vol 12 (20) ◽  
pp. 2045-2061 ◽  
Author(s):  
D. Peña Lara ◽  
J. A. Plascak
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field Theory ◽  
Mean Field ◽  
Pair Approximation ◽  
Temperature Anisotropy ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
The Mean

The general spin-S Blume–Capel model is studied within two different approaches: the pair approximation for the free energy, and Monte Carlo simulations. The global phase diagram in the temperature-anisotropy plane is obtained for general values of S in the pair approximation and the results are qualitatively the same as those of the usual mean field theory. Special interest is given in the low temperature region of the phase diagram where a number of first-order lines emerge from a multiphase point at the ground state. Monte Carlo simulations for S=1, 3/2, and 2 on simple cubic lattices also confirm the general trend of the mean field like approach, and in the special S=3/2 case the present results are in disagreement with previous Monte Carlo simulations, as well as renormalization group calculations on corresponding two-dimensional lattices.

scholarly journals RESHUFFLING SPINS WITH SHORT RANGE INTERACTIONS: WHEN SOCIOPHYSICS PRODUCES PHYSICAL RESULTS

2005 ◽  
Vol 16 (10) ◽  
pp. 1507-1517 ◽  
Author(s):  
A. O. SOUSA ◽  
K. MALARZ ◽  
S. GALAM
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Nonlinear Behavior ◽  
Opinion Dynamics ◽  
Monte Carlo Step ◽  
Square Lattice ◽  
The Mean ◽  
Dynamics Models

Galam reshuffling introduced in opinion dynamics models, is investigated under the nearest neighbor Ising model on a square lattice using Monte Carlo simulations. While the corresponding Galam analytical critical temperature TC≈3.09 [J/kB] is recovered almost exactly, it is proved to be different from both values, not reshuffled (TC =2/ arcsinh (1)≈2.27 [J/kB]) and mean-field (TC =4 [J/kB]). On this basis, gradual reshuffling is studied as function of 0≤p≤1 where p measures the probability of spin reshuffling after each Monte Carlo step. The variation of TC as function of p is obtained and exhibits a nonlinear behavior. The simplest Solomon network realization is noted to reproduce Galam p =1 result. Similarly to the critical temperature, critical exponents are found to differ from both, the classical Ising case and the mean field values.

Notizen: Monte-Carlo Simulation of a Two-dimensional Dipolar Lattice

1977 ◽  
Vol 32 (11) ◽  
pp. 1320-1322 ◽  
Author(s):  
S. Romano
Keyword(s):  
Monte Carlo ◽  
Mean Field Theory ◽  
Mean Field ◽  
Square Lattice ◽  
Electrostatic Energy ◽  
Two Dimensional ◽  
First Order ◽  
First Order Phase Transition ◽  
The Mean ◽  
First Order Phase

Abstract Monte-Carlo calculations were carried out on a system consisting of 256 point-dipoles, whose centres are fixed in a two-dimensional square lattice with the usual boundary con­dition; the Epstein-Ewald-Kornfeld algorithm was used in evaluating the electrostatic energy. No evidence of a first-order phase transition was found, and the results suggest there might be a second-order one. Additional calculations were carrierd out using the mean-field theory, which was found to overestimate the transition temperature by about a factor two.

scholarly journals A fractional generalization of the dirichlet distribution and related distributions

2021 ◽  
Vol 24 (1) ◽  
pp. 112-136
Author(s):  
Elvira Di Nardo ◽  
Federico Polito ◽  
Enrico Scalas
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Dirichlet Distribution ◽  
One Dimensional ◽  
Reasonable Approximation ◽  
Generalized Dirichlet Distribution ◽  
The One ◽  
Generalized Dirichlet

Abstract This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn ] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.

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