Partially Asymmetric Exclusion Models with Quenched Disorder

Juhász, Róbert; Santen, Ludger; Iglói, Ferenc

doi:10.1103/physrevlett.94.010601

Cited by 62 publications

(116 citation statements)

References 36 publications

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“…In the field of random walks, we have only described here the simplest models involving a single random walk in a disordered medium, but models involving many interacting random walks in the presence of quenched disorder can be also studied via the strong disorder approach [74], in particular reaction diffusion models [55,85], asymmetric exclusion processes [76], contact processes [70] and zero-range processes [77]. In the field of phase transitions of disordered polymer models, we have restricted our presentation here to the case of bidimensional wetting and of Poland-Scheraga model of DNA denaturation, but the idea to study the distribution of pseudo-critical temperatures allows to clarify the critical properties of other equilibrium transitions, such as the selective interface model [100] and the directed polymer transition in d = 3 [61] mentioned in the introduction (3).…”

Section: Discussionmentioning

confidence: 99%

Random Walks and Polymers in the Presence of Quenched Disorder

Monthus

2006

Lett Math Phys

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After a general introduction to the field, we describe some recent results concerning disorder effects on both 'random walk models', where the random walk is a dynamical process generated by local transition rules, and on 'polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures Tc(i, L) over the ensemble of samples (i) of size L. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.

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Section: Discussionmentioning

confidence: 99%

Random Walks and Polymers in the Presence of Quenched Disorder

Monthus

2006

Lett Math Phys

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“…In [12] it is shown that the ASEP on a periodic system may be mapped onto a Zero Range Process and the condensation transition is fully discussed in the context of the Zero Range Process. Recently, further progress has been made in understanding the case where q µ = 0 by using extreme values statistics and renormalisation arguments [161].…”

Section: Bose-einstein Condensationmentioning

confidence: 99%

Nonequilibrium steady states of matrix-product form: a solver's guide

Blythe

Evans²

2007

J. Phys. A: Math. Theor.

638

1,014

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Abstract. We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of this class of driven diffusive systems-which includes exclusion processes-focusing on interesting physical properties, such as shocks and phase transitions. We then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form. In addition to a gentle introduction to this matrix product approach, how it works and how it relates to similar constructions that arise in other physical contexts, we present a unified, pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed. We also review a number of more advanced topics, including nonequilibrium free energy functionals, the classification of exclusion processes involving multiple particle species, existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled. We conclude with a brief discussion of open problems for future research.

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“…Also reaction-diffusion models [11] with quenched disorder might show strong Griffiths effects [12], see, however [13,14]. As an example we consider here the PASEP with particle-wise (pw) disorder [8], in which the i-the particle, i = 1, 2, . .…”

Section: Introductionmentioning

confidence: 99%

“…Another class of problems with strong Griffiths effects are stochastic many-particle systems [6]) with quenched disorder [7], such as the 1d partially asymmetric simple exclusion process (PASEP)) with position or particle dependent hopping rates [8,9] or the zero range process (ZRP) with disorder [10]. Also reaction-diffusion models [11] with quenched disorder might show strong Griffiths effects [12], see, however [13,14].…”

Section: Introductionmentioning

confidence: 99%

Strong Griffiths singularities in random systems and their relation to extreme value statistics

2006

Self Cite

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We consider interacting many particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent, z, such as random quantum systems and exclusion processes. In several d = 1 and d = 2 dimensional problems we have calculated the inverse time-scales, τ −1 , in finite samples of linear size, L, either exactly or numerically. In all cases, having a discrete symmetry, the distribution function, P (τ −1 , L), is found to depend on the variable, u = τ −1 L z/d , and to be universal given by the limit distribution of extremes of independent and identically distributed random numbers. This finding is explained in the framework of a strong disorder renormalization group approach when, after fast degrees of freedom are decimated out the system is transformed into a set of non-interacting localized excitations. The Fréchet distribution of P (τ −1 , L) is expected to hold for all random systems having a strong disorder fixed point, in which the Griffiths singularities are dominated by disorder fluctuations.

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Partially Asymmetric Exclusion Models with Quenched Disorder

Cited by 62 publications

References 36 publications

Random Walks and Polymers in the Presence of Quenched Disorder

Random Walks and Polymers in the Presence of Quenched Disorder

Nonequilibrium steady states of matrix-product form: a solver's guide

Strong Griffiths singularities in random systems and their relation to extreme value statistics

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