On a Phase Separation Point for One - Dimensional Models

Ganikhodjaev, N. N.; Rozikov, U. A.

On a Phase Separation Point for One - Dimensional Models

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Description

In the paper a one-dimensional model with nearest - neighbor interactions $I_n, n\in \Z$ and spin values $\pm 1$ is considered. It is known that under some conditions on parameters $I_n$ the phase transition occurs for the model. We define a notion of "phase separation" point between two phases. We prove that the expectation value of the point is zero and its the mean square fluctuation is bounded by a constant $C(β)$ which tends to 1/4 if $β\to\infty$. Here $β=\frac{1}{T}$, $ T>0$-temperature.
10 pages