Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model

Nikolaos Fytas, Victor Martin-Mayor, Marco Picco, Nicolas Sourlas

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Abstract

We report a high-precision numerical estimation of the critical exponent α of the specific heat of the random-field Ising model in four dimensions. Our result \alpha = 0.12(1) indicates a diverging specific-heat behavior and is consistent with the estimation coming from the modified hyperscaling relation using our estimate of \theta via the anomalous dimensions \eta and \bar\eta. Our analysis benefited from a high-statistics zero-temperature numerical simulation of the model for two distributions of the random fields, namely a Gaussian and Poissonian distribution, as well as recent advances in finite-size scaling and reweighting methods for disordered systems. An original estimate of the critical slowing down exponent z of the maximum-flow algorithm used is also provided.
Original languageEnglish
Article number033302
Number of pages11
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2017
DOIs
Publication statusPublished - 6 Mar 2017

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Specific Heat
Random Field
Ising model
Ising Model
Exponent
specific heat
exponents
Higher statistics
Critical Slowing down
Disordered Systems
Maximum Flow
Finite-size Scaling
estimates
normal density functions
Estimate
Critical Exponents
Anomalous
statistics
scaling
Numerical Simulation

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Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model. / Fytas, Nikolaos; Martin-Mayor, Victor; Picco, Marco; Sourlas, Nicolas.

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, 033302, 06.03.2017.

Research output: Contribution to journalArticle

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