Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2006-08-14
Phys. Rev. B 77, 104429 (2008).
Physics
Condensed Matter
Disordered Systems and Neural Networks
50 pages, 18 figures, revised version
Scientific paper
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 yields 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.
Rizzo Tommaso
Yoshino Hajime
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