On a Phase Separation Point for One - Dimensional Models

Details On a Phase Separation Point for One - Dimensional Models On a Phase Separation Point for One - Dimensional Models

2007-08-09

arxiv.org/abs/0708.1212v1

Physics

Mathematical Physics

10 pages

Scientific paper

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 $C(\beta)$ which tends to 1/4 if $\beta\to\infty$. Here $\beta=\frac{1}{T}$, $ T>0$-temperature.

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