Volume 15, Issue 3
Numerical Analysis for a Mean-Field Equation for the Ising Model with Glauber Dynamics
DOI:

J. Comp. Math., 15 (1997), pp. 203-218

Published online: 1997-06

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• Abstract

In this paper, a mean-field equation of motion which is derived by Penrose (1991) for the dynamic Ising model with Glauber dynamics is considered. Various finite difference schemes such as explicit Euler scheme, predictor-corrector scheme and some implicit schemes are given and their convergence, stabilities and dynamical properties are discussed. Moreover, a Lyapunov functional for the discrete semigroup $\{ S\}_{n>0}$ is constructed. Finally, numerical examples are computed and analyzed. it shows that the model is a better approximation to Cahn-Allen equation which is mentioned in Penrose (1991).

• Keywords

@Article{JCM-15-203, author = {}, title = {Numerical Analysis for a Mean-Field Equation for the Ising Model with Glauber Dynamics}, journal = {Journal of Computational Mathematics}, year = {1997}, volume = {15}, number = {3}, pages = {203--218}, abstract = { In this paper, a mean-field equation of motion which is derived by Penrose (1991) for the dynamic Ising model with Glauber dynamics is considered. Various finite difference schemes such as explicit Euler scheme, predictor-corrector scheme and some implicit schemes are given and their convergence, stabilities and dynamical properties are discussed. Moreover, a Lyapunov functional for the discrete semigroup $\{ S\}_{n>0}$ is constructed. Finally, numerical examples are computed and analyzed. it shows that the model is a better approximation to Cahn-Allen equation which is mentioned in Penrose (1991). }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9200.html} }
TY - JOUR T1 - Numerical Analysis for a Mean-Field Equation for the Ising Model with Glauber Dynamics JO - Journal of Computational Mathematics VL - 3 SP - 203 EP - 218 PY - 1997 DA - 1997/06 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9200.html KW - AB - In this paper, a mean-field equation of motion which is derived by Penrose (1991) for the dynamic Ising model with Glauber dynamics is considered. Various finite difference schemes such as explicit Euler scheme, predictor-corrector scheme and some implicit schemes are given and their convergence, stabilities and dynamical properties are discussed. Moreover, a Lyapunov functional for the discrete semigroup $\{ S\}_{n>0}$ is constructed. Finally, numerical examples are computed and analyzed. it shows that the model is a better approximation to Cahn-Allen equation which is mentioned in Penrose (1991).