Finite-Size Scaling and Lack of Self-Averaging in Critical Disordered Systems

Wiseman, Shai; Domany, Eytan

doi:10.1103/physrevlett.81.22

Cited by 203 publications

(257 citation statements)

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“…In this case, it was argued [1,111] that eq. (40) should be replaced by ∆T c (L) ∼ L −1/νR for random critical points (41) i.e.…”

Section: Distribution Of Pseudo-critical Temperaturesmentioning

confidence: 99%

“…Important progresses have been made recently in the understanding of finite size properties of random critical points [1,2,10,102,110,111] . To each disordered sample (i) of size L, one should first associate a pseudo-critical temperature T c (i, L) [10,102,110,111].…”

Section: Distribution Of Pseudo-critical Temperaturesmentioning

confidence: 99%

“…To each disordered sample (i) of size L, one should first associate a pseudo-critical temperature T c (i, L) [10,102,110,111]. The disorder averaged pseudo-critical critical temperature…”

Section: Distribution Of Pseudo-critical Temperaturesmentioning

confidence: 99%

“…In terms of the correlation length ξ(T ), the following behaviour of R X (T, L) is expected [1,111] (i) off criticality, when L ≫ ξ(T ), the system can be divided into nearly independent sub-samples and this leads to 'Strong Self-Averaging'…”

mentioning

confidence: 99%

“…At criticality however, this 'subdivision' argument breaks down because of the divergence of ξ at T c , and a lack of self-averaging has been found at criticality whenever disorder is relevant [1,110,111]. More precisely, for a given observable X, it is convenient to define its normalized width as…”

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confidence: 99%

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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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“…In this case, it was argued [1,111] that eq. (40) should be replaced by ∆T c (L) ∼ L −1/νR for random critical points (41) i.e.…”

Section: Distribution Of Pseudo-critical Temperaturesmentioning

confidence: 99%

Section: Distribution Of Pseudo-critical Temperaturesmentioning

confidence: 99%

“…To each disordered sample (i) of size L, one should first associate a pseudo-critical temperature T c (i, L) [10,102,110,111]. The disorder averaged pseudo-critical critical temperature…”

Section: Distribution Of Pseudo-critical Temperaturesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Random Walks and Polymers in the Presence of Quenched Disorder

Monthus

2006

Lett Math Phys

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Computing Quantum Phase Transitions

Vojta

2008

Reviews in Computational Chemistry

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A phase transition occurs when the thermodynamic properties of a material display a singularity as a function of the external parameters. Imagine, for instance, taking a piece of ice out of the freezer. Initially, its properties change only slowly with increasing temperature. However, at 0°C, a sudden and dramatic change occurs. The thermal motion of the water molecules becomes so strong that it destroys the crystal structure. The ice melts, and a new phase of water forms, the liquid phase. At the phase transition temperature of 0°C the solid (ice) and the liquid phases of water coexist. A finite amount of heat, the so-called latent heat, is required to transform the ice into liquid water. Phase transitions involving latent heat are called first-order transitions. Another well known example of a phase transition is the ferromagnetic transition of iron. At room temperature, iron is ferromagnetic, i.e., it displays a spontaneous magnetization. With rising temperature, the magnetization decreases continuously due to thermal fluctuations of the spins.At the transition temperature (the so-called Curie point) of 770°C, the magnetization vanishes, and iron is paramagnetic at higher temperatures. In contrast to the previous example, there is no phase coexistence at the transition temperature; the ferromagnetic and paramagnetic phases rather become indistinguishable. Consequently, there is no latent heat. This type of phase transition is called continuous (second-order) transition or critical point.

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Critical points and quenched disorder: From Harris criterion to rare regions and smearing

Vojta

Sknepnek

2004

Physica Status Solidi (b)

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We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with sufficiently correlated disorder or in quantum systems with overdamped dynamics they can completely destroy the sharp phase transition by smearing. This is caused by effects similar to but stronger than Griffiths phenomena: True static order can develop on a rare region while the bulk system is still in the disordered phase. We discuss the thermodynamic behavior in the vicinity of such a smeared transition using optimal fluctuation theory, and we present numerical results for a two-dimensional model system.

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Finite-Size Scaling and Lack of Self-Averaging in Critical Disordered Systems

Cited by 203 publications

References 13 publications

Random Walks and Polymers in the Presence of Quenched Disorder

Random Walks and Polymers in the Presence of Quenched Disorder

Computing Quantum Phase Transitions

Critical points and quenched disorder: From Harris criterion to rare regions and smearing

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