On a Phase Separation Point for One - Dimensional Models

Abstract

In the paper a one-dimensional model with nearest - neighbor interactions $I_n,n\in \mathbb{Z}$ 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.

10 pages