Abstract
We study properties of the random configuration {s j (1)} N j=1 produced by the first step of the parallel dynamics in the Sherrington-Kirkpatrick model. We show that the law of large numbers holds for the sequence of overlaps between the initial (nonrandom) configuration {s j (0)} N j=1 and {s j (1)} N j=1 , and obtain the distribution of the fluctuations around the limiting value. As a by-product we derive the average number of the fixed points {s j (1)} Nj=1 with a given value of the magnetization\(m_N = (1/N)\sum\nolimits_{j = 1}^N {s_j (0)} \).
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Patrick, A.E. Dynamics in the Sherrington-Kirkpatrick model. I. The first step. J Stat Phys 84, 973–986 (1996). https://doi.org/10.1007/BF02174125
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DOI: https://doi.org/10.1007/BF02174125