On phase separation points for one-dimensional models |
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Authors: | N N Ganikhodjaev U A Rozikov |
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Institution: | (1) Institute of Mathematics and Information Technology, 100125 Tashkent, Uzbekistan;(2) International Islamic University, 25710 Kuantan, Malaysia;(3) School of Mathematical Sciences, GC University, Lahore, Pakistan |
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Abstract: | In the paper, the one-dimensional model with nearest-neighbor interactions I n , n ∈ Z, and the spin values ±1 is considered. It is known that, under some conditions on parameters of I n , a phase transition occurs for this model. We define the notion of a phase separation point between two phases. We prove that the expectation value of this point is zero and its mean-square fluctuation is bounded by a constant C(β) which tends to ¼ as β → ∞, where β = 1/T and T is the temperature. |
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Keywords: | one-dimensional Ising model with nearest-neighbor interactions phase separation point Gibbs measure |
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