### Abstract

Original language | English |
---|---|

Article number | 43003 |

Journal | Condensed Matter Physics |

Volume | 17 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 |

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### 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

### Cite this

*Condensed Matter Physics*,

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

**Random-field Ising model: Insight from zero-temperature simulations.** / Theodorakis, P.E.; Fytas, N.G.

Research output: Contribution to journal › Article

*Condensed Matter Physics*, vol. 17, no. 4, 43003. https://doi.org/10.5488/CMP.17.43003

}

TY - JOUR

T1 - Random-field Ising model: Insight from zero-temperature simulations

AU - Theodorakis, P.E.

AU - Fytas, N.G.

N1 - 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

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Finite-size scaling

KW - Graph theory

KW - Random-field Ising model

U2 - 10.5488/CMP.17.43003

DO - 10.5488/CMP.17.43003

M3 - Article

VL - 17

JO - Condensed Matter Physics

JF - Condensed Matter Physics

SN - 1607-324X

IS - 4

M1 - 43003

ER -