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

Abstract

We report a high-precision numerical estimation of the critical exponent $\alpha$ 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 form 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.

arXiv comment11 pages, 3 figures, 1 table. arXiv admin note: text overlap with arXiv:1512.06571

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