ISSN:
1572-9613
Keywords:
Ising model
;
master equation
;
clusters
;
nonlinear response
;
relaxation functions
;
biopolymers
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A one-dimensional kinetic Ising model with nearest neighbor interactionJ and magnetic fieldH ⩾ 0 is treated in both linear and nonlinear response, using the most general single spin-flip transition probabilities that depend on nearest neighbor states only. The dynamics is reformulated in terms of kinetic equations for the concentration nl +(t) [@#@ nl(t) of clusters containingl up- [or down-] spins, which is exact in the homogeneous case. The initial relaxation time τ* of the magnetization is obtained rigorously for arbitraryJ, H, and temperatureT. The relaxation function is found by numerical integration forJ/T 〈 2. It is shown that “coagulation” of minus-clusters becomes negligible for bothJ/T andH/T large, and the resulting set of equations is solved exactly in terms of an eigenvalue problem. A perturbation theory is developed to take into account the neglected coagulation terms. The relaxation function is found to be non-Lorentzian in general, in contrast to the Glauber results atH = 0, which are recovered as a special case. In addition, nonlinear and linear relaxation functions differ forH ≠ 0. Consequences for the application to biopolymers are briefly mentioned.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01014516
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