Finite-Size Scaling Approach to the Kinetic Ising Model(広領域の相転移物理学,研究会報告)

The kinetic Ising model on a square lattice is studied by means of the finite-size scaling with the help of the Monte Carlo method. The results obtained are consistent with the universality hypothesis that the value of the dynamic critical expotent is universal for certain types of transition probabilities. The present results also suggest that the dynamic critical exponents for the relaxation times of the magnetization and energy are the same. Our estimation of the dynamic critical exponent z gives that z \cong2.2 ±0.1.The kinetic Ising model on a square lattice is studied by means of the finite-size scaling with the help of the Monte Carlo method. The results obtained are consistent with the universality hypothesis that the value of the dynamic critical expotent is universal for certain types of transition probabilities. The present results also suggest that the dynamic critical exponents for the relaxation times of the magnetization and energy are the same. Our estimation of the dynamic critical exponent z gives that z \cong2.2 ±0.1.

Progress of Theoretical PhysicsAug 1, 198230 citations

Finite-size scaling of the three-dimensional Ising model

Robert Weston

Physics Letters BOct 1, 199011 citations

Finite-size calculations for the kinetic Ising model

Rahul Anil Pandit, Gabor Forgács, Pál Ruján

Using a Hamiltonian formulation of the master equation, we carry out finite-size calculations for the dynamical critical exponent $z$ of the kinetic Ising model in one and two dimensions. In one dimension, different appropriately normalized transition probabilities give different values for $z$ ; this result is based on both exact and finite-size calculations. We show that this "nonuniversal" behavior is due to the fact that the critical temperature for the one-dimensional Ising model is zero. In two dimensions we combine our finite-size calculations with finite-size scaling theory to calculate $z$ . Even in this case we find that $z$ depends on the form of the transition probability---a result that contradicts the universality hypothesis for dynamical critical behavior. We discuss the possible reasons for this contradiction.Using a Hamiltonian formulation of the master equation, we carry out finite-size calculations for the dynamical critical exponent $z$ of the kinetic Ising model in one and two dimensions. In one dimension, different appropriately normalized transition probabilities give different values for $z$; this result is based on both exact and finite-size calculations. We show that this "nonuniversal" behavior is due to the fact that the critical temperature for the one-dimensional Ising model is zero. In two dimensions we combine our finite-size calculations with finite-size scaling theory to calculate $z$. Even in this case we find that $z$ depends on the form of the transition probability---a result that contradicts the universality hypothesis for dynamical critical behavior. We discuss the possible reasons for this contradiction.

Physical review. B, Condensed matterAug 1, 19819 citations

Large-scale simulation of the two-dimensional kinetic Ising model

Andreas Linke, Dieter W. Heermann, Peter Altevogt +1 more

arXiv:cond-mat/9509115Physica A Statistical Mechanics and its ApplicationsDec 1, 199524 citations

Using a Hamiltonian formulation of the master equation, we carry out finite-size calculations for the dynamical critical exponent

z

of the kinetic Ising model in one and two dimensions. In one dimension, different appropriately normalized transition probabilities give different values for

z

; this result is based on both exact and finite-size calculations. We show that this "nonuniversal" behavior is due to the fact that the critical temperature for the one-dimensional Ising model is zero. In two dimensions we combine our finite-size calculations with finite-size scaling theory to calculate

z

. Even in this case we find that

z

depends on the form of the transition probability---a result that contradicts the universality hypothesis for dynamical critical behavior. We discuss the possible reasons for this contradiction.