Finite-Size Scaling and Correlation Lengths for Disordered Systems

Chayes, Jennifer; Chayes, L.; Fisher, Daniel S.; Spencer, Thomas

doi:10.1103/physrevlett.57.2999

Cited by 653 publications

(649 citation statements)

References 29 publications

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“…However the situation is different for finite systems. According to the general theorem for random systems [32] there exists a finite-size scaling correlation length ξ FS which characterizes the distribution of the observables in an ensemble of samples and which in principle has to be distinguished from the intrinsic correlation length ξ which enters into correlation functions. Approaching the critical point, the finite-size correlation length diverges similar to the intrinsic correlation length as ξ FS ∼ |f − f c | −νFS .…”

Section: Model and Frg Descriptionmentioning

confidence: 99%

Universal distribution of threshold forces at the depinning transition

2006

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We study the distribution of threshold forces at the depinning transition for an elastic system of finite size, driven by an external force in a disordered medium at zero temperature. Using the functional renormalization group (FRG) technique, we compute the distribution of pinning forces in the quasi-static limit. This distribution is universal up to two parameters, the average critical force, and its width. We discuss possible definitions for threshold forces in finite-size samples. We show how our results compare to the distribution of the latter computed recently within a numerical simulation of the so-called critical configuration.

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Section: Model and Frg Descriptionmentioning

confidence: 99%

Universal distribution of threshold forces at the depinning transition

2006

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“…However, this general bound has to be understood with the subtleties explained in [30]. In so-called 'conventional' random critical points, there is a single correlation length exponent ν = ν F S and this single exponent is expected to satisfy the bound.…”

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confidence: 99%

“…There exists a general bound for the finite-size correlation length exponent ν F S ≥ 2/d in disordered systems [30], which essentially means that a random critical point should itself be stable with respect to the addition of disorder, as in the Harris criterion argument given above. However, this general bound has to be understood with the subtleties explained in [30].…”

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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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“…One of the foremost arguments that disorder changes the critical behaviour of the CP is that it violates the Harris criterion [3,4] for all dimensions d < 4. This criterion states that a critical point is stable with respect to disorder if dν ⊥ > 2 where ν ⊥ is the critical exponent associated with the spatial correlation length.…”

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confidence: 99%

Contact process in heterogeneous and weakly disordered systems

2006

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The critical behavior of the contact process (CP) in heterogeneous periodic and weakly-disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents β (from series expansion) and η (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the directed percolation (DP) universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents.

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Finite-Size Scaling and Correlation Lengths for Disordered Systems

Cited by 653 publications

References 29 publications

Universal distribution of threshold forces at the depinning transition

Universal distribution of threshold forces at the depinning transition

Random Walks and Polymers in the Presence of Quenched Disorder

Contact process in heterogeneous and weakly disordered systems

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