Critical behavior of the ferromagneticq-state Potts model in fractal dimensions: Monte Carlo simulations on Sierpinski and Menger fractal structures

2006 ◽  
Vol 74 (9) ◽  
Author(s):  
Pascal Monceau
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Potts Model ◽  
Fractal Dimensions ◽  
Fractal Structures

scholarly journals Critical behavior of nonequilibrium models in short-time Monte Carlo simulations

2004 ◽  
Vol 70 (6) ◽  
Author(s):  
Roberto da Silva ◽  
Ronald Dickman ◽  
J. R. Drugowich de Felício
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Short Time ◽  
Nonequilibrium Models

Non-Equilibrium Critical Relaxation of Heisenberg Ferromagnets with Long-Range Correlated Defects

2012 ◽  
Vol 190 ◽  
pp. 39-42
Author(s):  
M. Medvedeva ◽  
Pavel V. Prudnikov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Initial State ◽  
Short Time ◽  
Theoretic Description ◽  
Good Agreement

The dynamic critical behavior of the three-dimensional Heisenberg model with longrangecorrelated disorder was studied by using short-time Monte Carlo simulations at criticality.The static and dynamic critical exponents are determined. The simulation was performed fromordered initial state. The obtained values of the exponents are in a good agreement with resultsof the field-theoretic description of the critical behavior of this model in the two-loopapproximation.

DYNAMICAL CRITICAL BEHAVIOR OF THE FOUR-DIMENSIONAL ISING MODEL

1996 ◽  
Vol 06 (06) ◽  
pp. 807-812 ◽  
Author(s):  
JOAN ADLER ◽  
DIETRICH STAUFFER
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Mean Field ◽  
Glauber Dynamics ◽  
Series Analysis ◽  
Logarithmic Corrections ◽  
Field Behavior

Monte Carlo simulations of the Glauber dynamics in the four-dimensional Ising model with up to 3124 spins agree with the theoretically expected logarithmic corrections to mean field behavior, if we assume J/kBTc = 0.14970, consistent with some series analysis.

scholarly journals Critical dynamics of the Potts model: short-time Monte Carlo simulations

2004 ◽  
Vol 333 (3-4) ◽  
pp. 277-283 ◽  
Author(s):  
Roberto da Silva ◽  
J.R. Drugowich de Felício
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Potts Model ◽  
Critical Dynamics ◽  
Short Time

SELF-ATTRACTING WALK ON NON-UNIFORM SUBSTRATES

2002 ◽  
Vol 16 (12) ◽  
pp. 449-457
Author(s):  
ZHI-JIE TAN ◽  
XIAN-WU ZOU ◽  
WEI ZHANG ◽  
SHENG-YOU HUANG ◽  
ZHUN-ZHI JIN
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Monte Carlo Simulations ◽  
Fractal Dimensions ◽  
Attractive Interaction ◽  
Percolation Clusters ◽  
Small Scales ◽  
End Distance ◽  
The Mean ◽  
End To End

Self-attracting walk (SATW) on non-uniform substrates has been investigated by Monte Carlo simulations. The non-uniform substrates are described by Leath percolation clusters with occupied probability p. p stands for the degree of non-uniformity, and takes on values in the range pc≲p ≤1 where pc is the threshold of percolation. For the case of strong attractive interaction u, p has little influence on the walk which is dominated by attractive interactions. Furthermore, in the case of small scales, the exponent ν of the mean end-to-end distance <R2(t)> versus time t is given by ν≃1/(ds+1), while the exponent k of visited sites versus t is given by k≃ds/(ds+1), where ds are the fractal dimensions of the substrates. For u ≃ 0, the walk reduces to the random walk on percolations with p in pc≲p≤1. Also, ν and k decrease sensitively with the reduction of p. It is found, the blocked sites in the substrates (i.e. defects) have much greater influence on the walk driven by thermal flunctuation than that dominated by the attractive interaction.

CRITICAL BEHAVIOR OF A FOUR-STATE IRREVERSIBLE MODEL WITH POTTS SYMMETRY

1999 ◽  
Vol 13 (14) ◽  
pp. 471-477 ◽  
Author(s):  
A. BRUNSTEIN ◽  
T. TOMÉ
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Critical Behavior ◽  
Potts Model ◽  
Present Model ◽  
Universality Class ◽  
Two Dimensional ◽  
Dynamical Phase ◽  
Dynamical Phase Transitions ◽  
Symmetry Operations

We analyze the critical behavior of a two-dimensional irreversible cellular automaton whose dynamic rules are invariant under the same symmetry operations as those of the three-state Potts model. We study the dynamical phase transitions that take place in the model and obtain the static and dynamical critical exponents through Monte Carlo simulations. Our results indicate that the present model is in the same universality class as the three-state Potts model.

scholarly journals Critical behavior of frustrated systems: Monte Carlo simulations versus renormalization group

JETP Letters ◽  
2000 ◽  
Vol 72 (6) ◽  
pp. 337-340 ◽  
Author(s):  
D. Loison ◽  
A. I. Sokolov ◽  
B. Delamotte ◽  
S. A. Antonenko ◽  
K. D. Schotte ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Frustrated Systems
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