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Interface in a one-dimensional Ising spin system. (English) Zbl 0849.60091

Summary: We will be studying the interface in a one-dimensional Ising spin system with a ferromagnetic Kac potential \(\gamma J(\gamma |r |)\). Below the critical temperature, when \(\gamma\) tends to 0, two distinct thermodynamic phases with different magnetizations appear. We will see that the local magnetization converges to one of these two values. On intervals of length \(\gamma^{- k}\) the local magnetization will stay almost constant, but on longer intervals interfaces take place between different phases. We prove first a large deviation principle and apply Freidlin and Wentzell theory to estimate the position where the first interface appears.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F10 Large deviations
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