Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model. Fytas, N. G., Martín-Mayor, V., Picco, M., & Sourlas, N. Journal of Statistical Mechanics: Theory and Experiment, 2017(3):033302, mar, 2017.
Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model [link]Paper  doi  abstract   bibtex   
We report a high-precision numerical estimation of the critical exponent \$}\backslashalpha{\$ of the specific heat of the random-field Ising model in four dimensions. Our result \$}\backslashalpha = 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 \$}\backslashtheta{\$ via the anomalous dimensions \$}\backslasheta{\$ and \$}\backslashbar{\{}\backslasheta{\}}{\$. 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.
@article{Fytas2016a,
abstract = {We report a high-precision numerical estimation of the critical exponent {\$}\backslashalpha{\$} of the specific heat of the random-field Ising model in four dimensions. Our result {\$}\backslashalpha = 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 {\$}\backslashtheta{\$} via the anomalous dimensions {\$}\backslasheta{\$} and {\$}\backslashbar{\{}\backslasheta{\}}{\$}. 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.},
archivePrefix = {arXiv},
arxivId = {1611.09015},
author = {Fytas, N.G. G. and Mart{\'{i}}n-Mayor, V. and Picco, M. and Sourlas, N.},
doi = {10.1088/1742-5468/aa5dc3},
eprint = {1611.09015},
file = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2016 - Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model.pdf:pdf},
issn = {1742-5468},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
keywords = {critical exponents and amplitudes,finite-size scaling,numerical simulations},
month = {mar},
number = {3},
pages = {033302},
title = {{Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model}},
url = {http://arxiv.org/abs/1611.09015 http://dx.doi.org/10.1088/1742-5468/aa5dc3 http://stacks.iop.org/1742-5468/2017/i=3/a=033302?key=crossref.2552d3aeac7d8d89add3a06895f23a08},
volume = {2017},
year = {2017}
}

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