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The replica method in liquid theory: from the basics to explicit computations

by Corrado Rainone

Submission summary

As Contributors: Corrado Rainone
Arxiv Link: http://arxiv.org/abs/1411.3941v2
Date submitted: 2017-09-10
Submitted by: Rainone, Corrado
Submitted to: SciPost Physics Lecture Notes
Domain(s): Theoretical
Subject area: Statistical and Soft Matter Physics

Abstract

In these notes we introduce briefly the fundamentals of the replica method in the context of liquid theory and the structural glass problem. In particular, we explain and show its usefulness as a computation framework in the context of the Random First Order Transition (RFOT) theory of the glass transition, whose defining points the reader is assumed to know. We shall give the intuitive idea of how and why the replica method is suitable for the description of the glass transition (the dynamical glass transition in particular) in real liquids, and then show how it can be used to make explicit computations and predictions that can be compared to experiments and numerical simulations.

Current status:

Undergoing voting at the Editorial College


Invited Reports on this Submission

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Anonymous Report 1 on 2017-10-29

Strengths

The paper is clear and written in a simple way.

Weaknesses

It lacks perspective.

Report

The replica method is a well developed technique to analyze glassy phases within mean-field theories of various refinements. Its role has been instrumental both in system with quenched disorder and in supercooled liquids and structural glasses, where quenched disorder is absent. This paper provides a mini-review of the replica method applied to structural glasses. Its scope is limited to explain the well known Monasson method (1995), and some of the simplest liquid theory approximations used to describe glassy phases in its conjunction. Some computations for the Mari-Kurchan model are presented. The review does not contain new results. The concepts are presented in a clear and elementary way, in this sense the paper could constitute an easy access point to neophytes. Unfortunately however, I find the discussion rather narrow and the choice of topics very limited. The paper does not even try to put the method into a broad physical perspective (in this case the one of the physics of glasses), which I think is a necessary ingredient of any review paper. Moreover, even at the level of glassy-replica theory, the most recent and important developments of glassy replica-theory -including the solution of the glass problem in infinite dimension- though mentioned are not discussed in detail. I do not see what this paper add to previous reviews on the subject e.g. the one by Parisi and Zamponi Rev. Mod. Phys. 82, 789 (2010). On the basis of that I cannot recommend publication on Sci-Post.

Requested changes

The paper should be completely revised to put it into a broad perspective in glassy physics and to include the last developments of the replica theory of glasses.

  • validity: low
  • significance: low
  • originality: low
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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