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Random-field Ising-like effective theory of the glass transition. I. Mean-field models

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Giulio Biroli, Chiara Cammarota, Gilles Tarjus, Marco Tarzia

Original languageEnglish
Article number174205
Pages (from-to)174205-1 - 174205-25
Number of pages25
JournalPhysical Review B
Volume98
Issue number17
DOIs
Accepted/In press19 Oct 2018
Published15 Nov 2018

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Abstract

In this paper, we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems - the overlap field with an equilibrium reference configuration - close to the putative thermodynamic glass transition. Our starting point is the mean-field theory of glass formation, which relies on the existence of a complex free-energy landscape with a multitude of metastable states. In this paper, we focus on archetypal mean-field models possessing this type of free-energy landscape and set up the framework to determine the exact effective theory. We show that the effective theory at the mean-field level is generically of the random-field + random-bond Ising type. We also discuss the main issues concerning the extension of our result to finite-dimensional systems. This extension is addressed in detail in the companion paper.

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