Lack of self-averaging in random systems—Liability or asset?

Efrat, Avishay; Schwartz, Moshe

doi:10.1016/j.physa.2014.06.071

Cited by 18 publications

(14 citation statements)

References 36 publications

(101 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On physical grounds, we have implemented a scaling approach based on the sample-to-sample fluctuations of the order parameter of the system. The outcome of this analysis indicated that the fluctuations of the system may be used as an alternative successful approach to criticality, as was also recently underlined by Efrat and Schwartz [60].…”

Section: Synopsissupporting

confidence: 61%

“…Our suggestion of employing the finite-size scaling behavior of the peaks of the sample-to-sample fluctuations of the order parameter was inspired by the intriguing analysis of Efrat and Schwartz [60]. These authors, studying also the d = 3 RFIM, showed that the behavior of the sample-to-sample fluctuations in a disordered system may be turned into a useful tool that can provide an independent measure to distinguish between the ordered and disordered phases of the system.…”

Section: Finite-size Scaling Analysismentioning

confidence: 99%

See 1 more Smart Citation

Universality in four-dimensional random-field magnets

Fytas

Theodorakis

2015

Eur. Phys. J. B

View full text Add to dashboard Cite

Abstract. We investigate the universality aspects of the four-dimensional random-field Ising model (RFIM) using numerical simulations at zero temperature. We consider two different, in terms of the field distribution, versions of the model, namely a Gaussian RFIM and an equal-weight trimodal RFIM. By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and system sizes. Using as finite-size measures the sample-to-sample fluctuations of the order parameter of the system, we propose, for both types of distributions, estimates of the critical field hc and the critical exponent ν of the correlation length, the latter suggesting that the two models in four dimensions share the same universality class. PACS

show abstract

Section: Synopsissupporting

confidence: 61%

Section: Finite-size Scaling Analysismentioning

confidence: 99%

Universality in four-dimensional random-field magnets

Fytas

Theodorakis

2015

Eur. Phys. J. B

View full text Add to dashboard Cite

show abstract

“…2 decreases as the system size increases [48][49][50][51][52][53][54][55][56]. This implies that in the thermodynamic limit, the result for a single sample agrees with the average over the whole ensemble of samples.…”

mentioning

confidence: 61%

“…This issue becomes particularly alarming as the system approaches the transition to the MBL phase [38,46,47]. If a quantity is non-self-averaging, the number of samples used in statistical analysis cannot be reduced as the system size increases [46,[48][49][50][51][52][53][54][55][56][57][58]. This reduction is a very common procedure due to the limited computational resources when dealing with exponentially large Hilbert spaces, but it may lead to wrong results.…”

mentioning

confidence: 99%

Multifractality and self-averaging at the many-body localization transition

Solórzano,

Santos,

Torres-Herrera

2021

Preprint

View full text Add to dashboard Cite

Finite-size effects have been a major and justifiable source of concern for studies of many-body localization, and several works have been dedicated to the subject. In this paper, however, we discuss yet another crucial problem that has received much less attention, that of the lack of selfaveraging and the consequent danger of reducing the number of random realizations as the system size increases. By taking this into account and considering ensembles with a large number of samples for all system sizes analyzed, we find that the generalized dimensions of the eigenstates of the disordered Heisenberg spin-1/2 chain close to the transition point to localization are described remarkably well by an exact analytical expression derived for the non-interacting Fibonacci lattice, thus providing an additional tool for studies of many-body localization.

show abstract

“…Exact calculations on hierarchical lattices are also currently widely used in a variety of statistical mechanics [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], finance [37], and, most recently, DNA-binding [38] problems.…”

Section: Renormalization-group Method: Migdal-kadanoff Approximamentioning

confidence: 99%

Phase transitions between different spin-glass phases and between different chaoses in quenched random chiral systems

Çağlar

Berker

2017

Phys. Rev. E

View full text Add to dashboard Cite

The left-right chiral and ferromagnetic-antiferromagnetic double-spin-glass clock model, with the crucially even number of states q = 4 and in three dimensions d = 3, has been studied by renormalization-group theory. We find, for the first time to our knowledge, four spin-glass phases, including conventional, chiral, and quadrupolar spin-glass phases, and phase transitions between spin-glass phases. The chaoses, in the different spin-glass phases and in the phase transitions of the spin-glass phases with the other spin-glass phases, with the non-spin-glass ordered phases, and with the disordered phase, are determined and quantified by Lyapunov exponents. It is seen that the chiral spin-glass phase is the most chaotic spin-glass phase. The calculated phase diagram is also otherwise very rich, including regular and temperature-inverted devil's staircases and reentrances.

show abstract

Lack of self-averaging in random systems—Liability or asset?

Cited by 18 publications

References 36 publications

Universality in four-dimensional random-field magnets

Universality in four-dimensional random-field magnets

Multifractality and self-averaging at the many-body localization transition

Phase transitions between different spin-glass phases and between different chaoses in quenched random chiral systems

Contact Info

Product

Resources

About