Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2022

The discrete random energy model and one step replica symmetry breaking

Résumé

We solve the random energy model when the energies of the configurations take only integer values. In the thermodynamic limit, the average overlaps remain size dependent and oscillate as the system size increases. While the extensive part of the free energy can still be obtained by a standard replica calculation with one step replica symmetry breaking, it is no longer possible to recover the overlaps in this way. A possible way to adapt the replica approach is to allow the sizes of the blocks in the Parisi matrix to fluctuate and to take complex values.

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Dates et versions

hal-03859136 , version 1 (13-06-2025)

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Bernard Derrida, Peter Mottishaw. The discrete random energy model and one step replica symmetry breaking. Journal of Physics A: Mathematical and Theoretical, 2022, 55 (26), pp.265002. ⟨10.1088/1751-8121/ac71e9⟩. ⟨hal-03859136⟩
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