ISSN:
1572-9613
Keywords:
Ising models
;
correlation functions
;
exclusion patterns
;
Markov processes
;
probability generating processes
;
large atoms
;
interacting atoms
;
partition functions
;
triangular lattice
;
rectangular lattice
;
disorder point
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract An anisotropic triangular Ising model in which the first- and second-order parameters and the field parameters are functionally related is solved exactly by representing the distribution of the atom patterns in terms of a suitably constructed Markov process. The probabilities of patterns, defined as the probabilities generated by this process, are a mathematically tractable alternative to the classical representation of these probabilities in terms of the partition function. The interaction and field parameters of this Ising model, its magnetization, free energy, and its nearest neighbor correlation functions, are expressed in terms of the parameters of this Markov process. Special cases are worked out in detail and numerical examples are given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01012878
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