of the metastable state of a 2-d kinetic Ising model. The model evolves under what is called a transition dynamic (TDA), which assumes that the system in going from an initial to a final state, must pass through an intermediate state t, such that the transition rate has the form, W ( i j) = W ( i t) W ( t j). The results are obtained in two different ways. First, by calculating the first-passage time from the metastable to an absorbing state. Second, by the technique of absorbing Markov chains. Our calculations reproduce the standard result obtained in the low-temperature nucleation regime, or = . However, we find that A and Γ differ from the values calculated for the standard Glauber dynamics. These results are consistent with recent studies which indicate that, contrary to common belief, Γ is not simply the metastable energy barrier, but depends on the stochastic dynamics used.]]>
, del estado metastable de un modelo cinético de Ising en 2-dimensiones. La evolución del sistema viene dada por una dinámica de transición (TDA) que asume que el sistema para poder pasar de un estado inicial a uno final debe pasar por un estado intermedio t, tal que la probabilidad de transición es de la forma W (i j) = W( i t) W ( tj). Los resultados son obtenidos de dos formas distintas. Una del cálculo del tiempo que toma el sistema metaestable en pasar por primera vez a un estado absorbente. La otra utilizando la técnica de las cadenas absorbentes de Markov. Nuestros cálculos reproducen el resultado estandard que dice que, a bajas temperaturas, en el regimen de nucleación, o = . Sin embargo encontramos que A y Γ son distintos de los obtenidos para la dinámica estandard de Glauber. Estos resultados son consistentes con estudios recientes que prueban que, al contrario a lo que se creia, Γ no es simplemente la barrera de energía metastable sino que depende de la dinamica estocástica utilizada.]]>
Física Estadística
Metastable lifetime of a kinetic Ising model with a transition dynamic algorithm
G.M. Buendía*, P.A. Rikvold**, K. Park*** and M.A. Novotny****
* Department of Physics, Universidad Simón Bolívar, Caracas 1080, Venezuela
** School of Computational Science and Information Technology, Center for Materials Research and Department of Physics, Florida State University, Tallahassee, FL 32306–435, USA
*** Center for Computational Science, Naval Research Laboratory, Washington DC. 20375, USA
**** Department of Physics and Astronomy and ERC Center for Computational Sciences, Mississippi State University MS 39762, USA
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Recibido el 23 de noviembre de 2003 Aceptado el 2 de mayo de 2004
Abstract
We calculate the average lifetime of the metastable state of a 2–d kinetic Ising model. The model evolves under what is called a transition dynamic (TDA), which assumes that the system in going from an initial to a final state, must pass through an intermediate state t, such that the transition rate has the form, W ( i j) = W ( i t) W ( t j). The results are obtained in two different ways. First, by calculating the first–passage time from the metastable to an absorbing state. Second, by the technique of absorbing Markov chains. Our calculations reproduce the standard result obtained in the low–temperature nucleation regime, = . However, we find that A and Γ differ from the values calculated for the standard Glauber dynamics. These results are consistent with recent studies which indicate that, contrary to common belief, Γ is not simply the metastable energy barrier, but depends on the stochastic dynamics used.
Calculamos la vida media , del estado metastable de un modelo cinético de Ising en 2–dimensiones. La evolución del sistema viene dada por una dinámica de transición (TDA) que asume que el sistema para poder pasar de un estado inicial a uno final debe pasar por un estado intermedio t, tal que la probabilidad de transición es de la forma W (ij) = W( i t) W ( tj). Los resultados son obtenidos de dos formas distintas. Una del cálculo del tiempo que toma el sistema metaestable en pasar por primera vez a un estado absorbente. La otra utilizando la técnica de las cadenas absorbentes de Markov. Nuestros cálculos reproducen el resultado estandard que dice que, a bajas temperaturas, en el regimen de nucleación, = . Sin embargo encontramos que A y Γ son distintos de los obtenidos para la dinámica estandard de Glauber. Estos resultados son consistentes con estudios recientes que prueban que, al contrario a lo que se creia, Γ no es simplemente la barrera de energía metastable sino que depende de la dinamica estocástica utilizada.
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Descriptores: Metaestabilidad; nucleación; modelo cinético de Ising.
1. F.F. Abraham, Homogeneous Nucleation Theory (Academic, New York, 1974). [ Links ]
2. M.A. Novotny, G. Brown, and P.A. Rikvold, J. Appl. Phys. 91 (2002) 6908; [ Links ] P.A. Rikvold and B.M. Gorman, in Annual Reviews of Computational Physics I, Ed. D. Stauffer (World Scientific, Singapure, 1994). [ Links ]
3. E. Jordao Neves and R.H. Schonmann, Commun. Math. Phys. 137 (1991) 209. [ Links ]
j) = W ( i
or = 
. However, we find that A and Γ differ from the values calculated for the standard Glauber dynamics. These results are consistent with recent studies which indicate that, contrary to common belief, Γ is not simply the metastable energy barrier, but depends on the stochastic dynamics used.]]>
of the metastable state of a 2–d kinetic Ising model. The model evolves under what is called a transition dynamic (TDA), which assumes that the system in going from an initial to a final state, must pass through an intermediate state t, such that the transition rate has the form, W ( i
j) = W ( i
. However, we find that A and Γ differ from the values calculated for the standard Glauber dynamics. These results are consistent with recent studies which indicate that, contrary to common belief, Γ is not simply the metastable energy barrier, but depends on the stochastic dynamics used.