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.

ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A JUNCTION: THE EFFECT OF UNEQUAL INJECTION RATES

2009 ◽  
Vol 20 (06) ◽  
pp. 967-978 ◽  
Author(s):  
XIONG WANG ◽  
RUI JIANG ◽  
KATSUHIRO NISHINARI ◽  
MAO-BIN HU ◽  
QING-SONG WU
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Exclusion Processes ◽  
Asymmetric Exclusion ◽  
Asymmetric Exclusion Processes ◽  
Injection Rates

Asymmetric exclusion processes (ASEP) on lattices with a junction, in which two or more parallel lattice branches combine into a single one, is important as a model for complex transport phenomena. This paper investigates the effect of unequal injection rates in ASEP with a junction. It is a generalization of the work of Pronina and Kolomeisky [J. Stat. Mech. P07010 (2005)], in which only equal injection rates are considered. It is shown that the unequal rates give rise to new phases and the phase diagram structure is qualitatively changed. The phase diagram and the density profiles are investigated by using Monte Carlo simulations, mean field approximation and domain wall approach. The analytical results are in good agreement with Monte Carlo simulations.

scholarly journals Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition

2022 ◽  
Vol 2022 (1) ◽  
pp. 013402
Author(s):  
Xiang Li ◽  
Mauro Mobilia ◽  
Alastair M Rucklidge ◽  
R K P Zia
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Social Interaction ◽  
Monte Carlo Simulations ◽  
Network Structure ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Analysis ◽  
Long Time

Abstract We investigate the long-time properties of a dynamic, out-of-equilibrium network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents’ opinions are fixed, they have a preferred degree which leads them to endlessly create and delete links. Our evolving network is shaped by homophily/heterophily, a form of social interaction by which individuals tend to establish links with others having similar/dissimilar opinions. Using Monte Carlo simulations and a detailed mean-field analysis, we investigate how the sizes of the communities and the degree of homophily/heterophily affect the network structure. In particular, we show that when the network is subject to enough heterophily, an ‘overwhelming transition’ occurs: individuals of the smaller community are overwhelmed by links from the larger group, and their mean degree greatly exceeds the preferred degree. This and related phenomena are characterized by the network’s total and joint degree distributions, as well as the fraction of links across both communities and that of agents having fewer edges than the preferred degree. We use our mean-field theory to discuss the network’s polarization when the group sizes and level of homophily vary.

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