Fluctuations in a spin-glass model with one replica symmetry breaking

We study statistical properties of peculiar responses in glassy systems at mesoscopic scales based on a class of mean-field spin-glass models which exhibit 1 step replica symmetry breaking. Under variation of a generic external field, a finite-sized sample of such a system exhibits a series of step wise responses which can be regarded as a finger print of the sample. We study in detail the statistical properties of the step structures based on a low temperature expansion approach and a replica approach. The spacings between the steps vanish in the thermodynamic limit so that arbitrary small but finite variation of the field induce infinitely many level crossings in the thermodynamic limit leading to a static chaos effect which yeilds a self-averaging, smooth macroscopic response. We also note that there is a strong analogy between the problem of step-wise responses in glassy systems at mesoscopic scales and intermittency in turbulent flows due to shocks.

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“…Especially it has been pointed out [57,58] that if one computes the heat capacity from the thermal fluctuations of energy E via FDT: (1/N )β 2 E…”

Section: Appendix G: Fluctuations Of Clusters In One-step Rsb Solutionsmentioning

confidence: 99%

“…It has been suggested [57,58,59] that one then must consider fluctuations from the saddle point, in particular, the size of clusters m explicitly.…”

Section: Appendix G: Fluctuations Of Clusters In One-step Rsb Solutionsmentioning

confidence: 99%

Stepwise responses in mesoscopic glassy systems: A mean-field approach

Yoshino

Rizzo

2008

Phys. Rev. B

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“…Trying to predict finite size corrections of disordered systems which exhibit broken replica symmetry has been a long standing problem [3,4,5,6]. If one uses the replica approach the difficulty comes from the fact that one needs to deal with a quadratic form around a saddle point in a space with a non integer number of dimensions.…”

Section: Introductionmentioning

confidence: 99%

Finite Size Corrections to the Parisi Overlap Function in the GREM

Derrida

Mottishaw

2018

J Stat Phys

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We investigate the effects of finite size corrections on the overlap probabilities in the Generalized Random Energy Model (GREM) in two situations where replica symmetry is broken in the thermodynamic limit. Our calculations do not use replicas, but shed some light on what the replica method should give for finite size corrections. In the gradual freezing situation, which is known to exhibit full replica symmetry breaking, we show that the finite size corrections lead to a modification of the simple relations between the sample averages of the overlaps Y k between k configurations predicted by replica theory. This can be interpreted as fluctuations in the replica block size with a negative variance. The mechanism is similar to the one we found recently in the random energy model [1]. We also consider a simultaneous freezing situation, which is known to exhibit one step replica symmetry breaking. We show that finite size corrections lead to full replica symmetry breaking and give a more complete derivation of the results presented in [2] for the directed polymer on a tree.

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“…The study of the first-order transition which occurs at mean-field level requires the inclusion of terms quartic in the q fields, but these are ''irrelevant'' variables at the presumed continuous transition in finite dimensions and they will be dropped. At the mean-field level, the transition is continuous if w 2 =w 1 1 [4]. In the p-spin replicated functional of Eq.…”

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confidence: 99%