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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2022

Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case

Résumé

We analyze the top Lyapunov exponent of the product of sequences of two by two matrices that appears in the analysis of several statistical mechanics models with disorder: for example these matrices are the transfer matrices for the nearest neighbor Ising chain with random external field, and the free energy density of this Ising chain is the Lyapunov exponent we consider. We obtain the sharp behavior of this exponent in the large interaction limit when the external field is centered: this balanced case turns out to be critical in many respects. From a mathematical standpoint we precisely identify the behavior of the top Lyapunov exponent of a product of two dimensional random matrices close to a diagonal random matrix for which top and bottom Lyapunov exponents coincide. In particular, the Lyapunov exponent is only log-Hölder continuous.
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Dates et versions

hal-03912135 , version 1 (23-12-2022)

Identifiants

Citer

Giambattista Giacomin, Rafael Greenblatt. Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2022, 19 (1), pp.701-728. ⟨10.30757/alea.v19-27⟩. ⟨hal-03912135⟩
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