TY - JOUR
T1 - Generalized moment expansion of dynamic correlation functions in finite Ising systems
AU - Bauer, Hans Ulrich
AU - Schulten, Klaus
AU - Nadler, Walter
N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1988
Y1 - 1988
N2 - In this paper we study dynamic correlation functions of one- and two-dimensional kinetic Ising models, in particular, in situations where nonergodic behavior and critical slowing down emerge. We also investigate in how far nonexponential relaxation as described by a Williams-Watts function exp[-(t/)] results in such systems. The method we apply is an expansion which simultaneously takes the high- and low-frequency behavior of observables into account (generalized moment expansion). This approximation can be applied to kinetic Ising models with arbitrary transition rate constants. Its computational effort does not increase when relaxation times diverge. However, the method involves the inversion of the transition operator and, hence, can be applied only to finite systems, the size of which depends on computational resources. We introduce a coarse graining of the state space which allows to extend the system size further and yields accurate magnetization correlation functions.
AB - In this paper we study dynamic correlation functions of one- and two-dimensional kinetic Ising models, in particular, in situations where nonergodic behavior and critical slowing down emerge. We also investigate in how far nonexponential relaxation as described by a Williams-Watts function exp[-(t/)] results in such systems. The method we apply is an expansion which simultaneously takes the high- and low-frequency behavior of observables into account (generalized moment expansion). This approximation can be applied to kinetic Ising models with arbitrary transition rate constants. Its computational effort does not increase when relaxation times diverge. However, the method involves the inversion of the transition operator and, hence, can be applied only to finite systems, the size of which depends on computational resources. We introduce a coarse graining of the state space which allows to extend the system size further and yields accurate magnetization correlation functions.
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U2 - 10.1103/PhysRevB.38.445
DO - 10.1103/PhysRevB.38.445
M3 - Article
AN - SCOPUS:5644257517
VL - 38
SP - 445
EP - 458
JO - Physical Review B
JF - Physical Review B
SN - 0163-1829
IS - 1
ER -