One-dimensional Markovian-field Ising model: physical properties and characteristics of the discrete stochastic mapping
- 7 May 1988
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (9) , 2151-2165
- https://doi.org/10.1088/0305-4470/21/9/028
Abstract
The zero-temperature physical properties of an Ising chain in a Markovian field taking only two values with non-zero mean are evaluated and a related discrete stochastic mapping with the theory of finite Markov chains is investigated. A discontinuous behaviour of the magnetisation and the residual entropy, dependent on both mean field and exchange, is found which can be related to flips of microscopic spin clusters. For non-zero temperature the mapping is characterised by the fractal properties of its attractor and by the Lyapunov exponent. An explicit expression for the measure in the nth iteration of the Chapman-Kolmogorov equation is obtained.Keywords
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