### Abstract

We enlighten some critical aspects of the three-dimensional (d = 3) random-field Ising model from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian random-field Ising model and an equal-weight trimodal random-field Ising model. By implementing a computational approach thatmaps the ground-state of the systemto themaximum-flowoptimization 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 systems sizesV = L ×L ×L, where L denotes linear lattice size and Lmax = 156. Using as finite-size measures the sample to- sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field hc and the critical exponent v of the correlation length, the latter clearly suggesting that both models share the same universality class. Additional simulations of the Gaussian random-field Ising model at the best-known value of the critical field provide the magnetic exponent ratio β/v with high accuracy and clear out the controversial issue of the critical exponent α of the specific heat. Finally, we discuss the infinite-limit size extrapolation of energy and order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.

Original language | English |
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Article number | 43003 |

Journal | Condensed Matter Physics |

Volume | 17 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 |

### Bibliographical note

This article is published in an open access journal and is available to download at: http://www.icmp.lviv.ua/journal/zbirnyk.80/43003/art43003.pdf### Keywords

- Finite-size scaling
- Graph theory
- Random-field Ising model

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## Cite this

Theodorakis, P. E., & Fytas, N. G. (2014). Random-field Ising model: Insight from zero-temperature simulations.

*Condensed Matter Physics*,*17*(4), [43003]. https://doi.org/10.5488/CMP.17.43003