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One-dimensional random field Ising model and discrete stochastic mappings
Authors:U. Behn  V. A. Zagrebnov
Affiliation:(1) Karl-Marx-Platz, Sektion Physik der Karl-Marx-Universität Leipzig, 7010 Leipzig, German Democratic Republic;(2) Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, USSR
Abstract:Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.Contribution to the symposium ldquoStatistical Mechanics of Phase Transitions—Mathematical and Physical Aspects,rdquo Treboncaron, CSSR, September 1–6, 1986.
Keywords:Random field Ising model  stochastic mapping  Markov chains  invariant measure  fractal dimension
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