Hans-Ulrich Bauer, Klaus Schulten, and Walter Nadler.
Generalized moment expansion of dynamic correlation functions in
finite Ising systems.
Physical Review B, 38:445-458, 1988.
BAUE88
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
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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