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.
|Number of pages||11|
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|Publication status||Published - 6 Mar 2017|
Fytas, N., Martin-Mayor, V., Picco, M., & Sourlas, N. (2017). Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model. Journal of Statistical Mechanics: Theory and Experiment, 2017, . https://doi.org/10.1088/1742-5468/aa5dc3