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Replica Method and Finite Volume Corrections

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Abstract

In this note we introduce a method to calculate the finite volume corrections to the mean field results for the free energy when replica symmetry is broken at one-step. We find that the naive results are modified by the presence of additional corrections: these corrections can be interpreted as arising from fluctuations in the size of the blocks in the replica approach. The computation suggests a new approach for deriving the replica broken results in a rigorous way.

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Authors and Affiliations

  1. Dipartimento di Fisica, INFN, Statistical Mechanics and Complexity Center (SMC)–INFM–CNR, Università di Roma “La Sapienza”, Piazzale A. Moro 2, 00185, Rome, Italy

    Matteo Campellone, Giorgio Parisi & Miguel Angel Virasoro

Authors
  1. Matteo Campellone
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  2. Giorgio Parisi
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  3. Miguel Angel Virasoro
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Correspondence to Giorgio Parisi.

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Campellone, M., Parisi, G. & Virasoro, M.A. Replica Method and Finite Volume Corrections. J Stat Phys 138, 29–39 (2010). https://doi.org/10.1007/s10955-009-9891-1

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  • DOI: https://doi.org/10.1007/s10955-009-9891-1

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