Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-07-10
Phys. Rev. E 66, 041102 (2002)
Physics
Condensed Matter
Statistical Mechanics
10 pages Revtex (two-column), 1 eps figure (included)
Scientific paper
10.1103/PhysRevE.66.041102
We compute exactly the distribution of the occupation time in a discrete {\em non-Markovian} toy sequence which appears in various physical contexts such as the diffusion processes and Ising spin glass chains. The non-Markovian property makes the results nontrivial even for this toy sequence. The distribution is shown to have non-Gaussian tails characterized by a nontrivial large deviation function which is computed explicitly. An exact mapping of this sequence to an Ising spin glass chain via a gauge transformation raises an interesting new question for a generic finite sized spin glass model: at a given temperature, what is the distribution (over disorder) of the thermally averaged number of spins that are aligned to their local fields? We show that this distribution remains nontrivial even at infinite temperature and can be computed explicitly in few cases such as in the Sherrington-Kirkpatrick model with Gaussian disorder.
Dean David S.
Majumdar Satya N.
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