Short Time Dynamics of an Irreversible Probabilistic Cellular Automaton

1998 ◽  
Vol 12 (21) ◽  
pp. 873-879 ◽  
Author(s):  
T. Tomé ◽  
J. R. Drugowich de Fel Icio
Keyword(s):  
Ising Model ◽  
Cellular Automaton ◽  
Early Time ◽  
Universality Class ◽  
Kinetic Ising Model ◽  
Time Dynamics ◽  
Probabilistic Cellular Automaton ◽  
Time Regime ◽  
The One ◽  
Short Time

We study the short-time dynamics of a three-state probabilistic cellular automaton. This automaton, termed TD model, possess "up-down" symmetry similar to Ising models, and displays continuous kinetic phase transitions belonging to the Ising model universality class. We perform Monte Carlo simulations on the early time regime of the two-dimensional TD model at criticality and obtain the dynamic exponent θ associated to this regime, and the exponents β/ν and z. Our results indicate that, although the model do not possess microscopic reversibility, it presents short-time universality which is consistent with the one of the kinetic Ising model.

SHORT TIME CORRELATIONS IN A TWO-DIMENSIONAL ISING MODEL WITH A LINE OF DEFECTS

2001 ◽  
Vol 15 (25) ◽  
pp. 1141-1146 ◽  
Author(s):  
T. TOMÉ ◽  
C. S. SIMÕES ◽  
J. R. DRUGOWICH DE FELÍCIO
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Ising Model ◽  
Early Time ◽  
Time Correlation ◽  
Two Dimensional ◽  
Time Dynamics ◽  
Time Correlations ◽  
Time Regime ◽  
Short Time

We study the short time dynamics of a two-dimensional Ising model with a line of defects. The dynamical critical exponent θ associated to the early time regime at the critical temperature was obtained by Monte Carlo simulations. The exponent θ was estimated by a method where the quantity of interest is the time correlation of the magnetization.

scholarly journals Early-time regime for interfacial instabilities in a kinetic Ising model

1993 ◽  
Vol 48 (6) ◽  
pp. 4592-4598 ◽  
Author(s):  
Loki Jörgenson ◽  
H. Guo ◽  
R. Harris ◽  
M. Grant
Keyword(s):  
Ising Model ◽  
Early Time ◽  
Interfacial Instabilities ◽  
Kinetic Ising Model ◽  
Time Regime

DETERMINATION OF THE VAPOR-LIQUID CRITICAL POINT FROM THE SHORT-TIME DYNAMICS

2001 ◽  
Vol 15 (12n13) ◽  
pp. 369-374 ◽  
Author(s):  
SHENG-YOU HUANG ◽  
XIAN-WU ZOU ◽  
ZHI-JIE TAN ◽  
ZHUN-ZHI JIN
Keyword(s):  
Critical Point ◽  
Early Time ◽  
Dynamic Scaling ◽  
Time Behavior ◽  
Time Dynamic ◽  
Time Dynamics ◽  
Dynamics Simulations ◽  
Average Potential Energy ◽  
Short Time ◽  
Vapor Liquid

Considering the average potential energy per particle as the parameter, we investigate the early-time dynamics of vapor-liquid transition in the critical region for 2D Lennard-Jones fluids by using NVT molecular dynamics simulations. The results verify the existence of short-time dynamic scaling in the fluid systems and show that the critical point Tc can be determined by the universal short-time behavior. The obtained value of Tc = 0.540 from the short-time dynamics is very close to the value of 0.533 from the Monte Carlo simulations in the equilibrium state of the systems.

An Analytical Approach to the Fredrickson–Andersen Model in One Dimension

1997 ◽  
Vol 11 (24) ◽  
pp. 2927-2940 ◽  
Author(s):  
Michael Schulz ◽  
Steffen Trimper
Keyword(s):  
Ising Model ◽  
Evolution Equations ◽  
Fock Space ◽  
One Dimension ◽  
Space Representation ◽  
Short Time Scale ◽  
Kinetic Ising Model ◽  
Andersen Model ◽  
Long Time ◽  
Short Time

The dynamics of a modified kinetic Ising model usual noted as Fredrickson–Andersen model (FAM) is formulated in terms of Pauli-operators using a Fock-space representation of the Master equation. The method is appropriate to study the cooperativity by including topological restrictions explicitly. Following the concept of the FAM the block distribution function of m+1 adjacent liquid-like (spin down) or solid-like (spin up) regions is analysed in one dimension. The hierarchy of evolution equations for those functions can be solved exactly at zero temperature leading to a double exponential decay and to a nonergodic behaviour. In case of nonzero temperatures, we are able to solve this set of infinite nonlinear first order differential equations only after a well motivated decoupling procedure. It results an implicit solution for the averaged density. For short time scale the system behaves like an ordinary Ising model with exponential relaxation. In the long time limit, we observe already in lowest order a crossover to an exponential screened algebraic decay with an universal exponent 3/2 and moreover, the relaxation time will be drastically enlarged.

The two-dimensional site-diluted Ising model: a short-time-dynamics approach

2009 ◽  
Vol 21 (34) ◽  
pp. 346005 ◽  
Author(s):  
L F da Silva ◽  
U L Fulco ◽  
F D Nobre
Keyword(s):  
Ising Model ◽  
Two Dimensional ◽  
Time Dynamics ◽  
Short Time

scholarly journals DYNAMIC CRITICAL EXPONENTS OF THE ISING MODEL WITH MULTISPIN INTERACTIONS

2001 ◽  
Vol 15 (15) ◽  
pp. 487-496 ◽  
Author(s):  
C. S. SIMÕES ◽  
J. R. DRUGOWICH DE FELÍCIO
Keyword(s):  
Ising Model ◽  
Potts Model ◽  
Critical Exponents ◽  
Finite Size ◽  
Two Dimensions ◽  
Time Dynamics ◽  
Spin Interactions ◽  
Dynamic Exponent ◽  
Short Time ◽  
Multispin Interactions

We revisit the short-time dynamics of 2D Ising model with three spin interactions in one direction and estimate the critical exponents z, θ, β and ν. Taking properly into account the symmetry of the Hamiltonian, we obtain results completely different from those obtained by Wang et al.10 For the dynamic exponent z our result coincides with that of the 4-state Potts model in two dimensions. In addition, results for the static exponents ν and β agree with previous estimates obtained from finite size scaling combined with conformal invariance. Finally, for the new dynamic exponent θ we find a negative and close to zero value, a result also expected for the 4-state Potts model according to Okano et al.

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