PMID: 11308545Apr 20, 2001Paper

Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in Liouville and sinh-Gordon models

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
D Carpentier, Pierre Le Doussal

Abstract

We study via renormalization group (RG), numerics, exact bounds, and qualitative arguments the equilibrium Gibbs measure of a particle in a d-dimensional Gaussian random potential with translationally invariant logarithmic spatial correlations. We show that for any d>/=1 it exhibits a transition at T=T(c)>0. The low-temperature glass phase has a nontrivial structure, being dominated by a few distant states (with replica symmetry breaking phenomenology). In finite dimension this transition exists only in this "marginal glass" case (energy fluctuation exponent straight theta=0) and disappears if correlations grow faster (single ground-state dominance straight theta>0) or slower (high-temperature phase). The associated extremal statistics problem for correlated energy landscapes exhibits universal features which we describe using a nonlinear Kolmogorov (KPP) RG equation. These include the tails of the distribution of the minimal energy (or free energy) and the finite-size corrections, which are universal. The glass transition is closely related to Derrida's random energy models. In d=2, the connection between this problem and Liouville and sinh-Gordon models is discussed. The glass transition of the particle exhibits interesting s...Continue Reading

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Citations

Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pierre Le DoussalPascal Chauve
Jun 1, 2001·Physical Review Letters·H E Castillo, P Le Doussal
Nov 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D S Dean, S N Majumdar
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T AntalZ Rácz
Jul 13, 2004·Physical Review Letters·Satya N Majumdar, Alain Comtet
Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J F MuzyA Kozhemyak
Jul 30, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Joachim Rambeau, Grégory Schehr
Mar 10, 2012·Physical Review Letters·Grégory Schehr, Satya N Majumdar
Jun 12, 2012·Physical Review Letters·Yan V FyodorovJonathan P Keating
Dec 18, 2013·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Yan V Fyodorov, Jonathan P Keating
Nov 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Debabrata Panja
Jun 13, 2020·Physical Review Letters·Yan V Fyodorov, Pierre Le Doussal
Mar 18, 2017·Physical Review Letters·Xiangyu CaoPierre Le Doussal
Dec 17, 2004·Physical Review Letters·Gregory Schehr, Pierre Le Doussal
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Cécile Monthus
Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·David B Saakian
May 1, 2012·Physical Review Letters·Olalla A Castro-Alvaredo, Benjamin Doyon
May 17, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·David B Saakian
Mar 21, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Cécile Monthus, Thomas Garel
Nov 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Clément Sire, Pierre-Henri Chavanis
Sep 28, 2004·Physical Review Letters·C J Bolech, Alberto Rosso
Jan 7, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jean-François Muzy, Emmanuel Bacry
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Cécile Monthus, Thomas Garel
Mar 23, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Himanshu Agrawal, Deepak Dhar
Apr 10, 2021·Physical Review Letters·Xiangyu Cao, Raoul Santachiara

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