2006
DOI: 10.1103/physrevb.74.064418
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Numerical study of the three-dimensional random-field Ising model at zero and positive temperature

Abstract: In this paper the three-dimensional random-field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling analysis of large discontinuities in the bond energy. The heat capacity exponent ␣ is found to be near zero. The ground states are determined for a range of external field and disorder strength near the zero temperature critical point and the scaling of ground state tilings of the field-disorder plane is discussed.… Show more

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Cited by 38 publications
(45 citation statements)
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“…Those of set A are slightly larger as a consequence of the more strict criterion, P min < 0.75, used for the identification of the dp RF realizations. The interesting first-order-like properties of the model, reported by Hernández and Diep [34] and Hernández and Ceva [35] for the bimodal RFIM and by Wu and Machta [28] for the Gaussian RFIM, have added more complication and novelty to the RFIM. The first-order-like characteristics of the Gaussian RFIM found by Wu and Machta [28] revealed that the appearance of these strong finite-size effects are independent of the RF distribution and their existence is related to the value of the disorder strength.…”
Section: Revisiting the Order Of The Transition By The High-level Onementioning
confidence: 95%
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“…Those of set A are slightly larger as a consequence of the more strict criterion, P min < 0.75, used for the identification of the dp RF realizations. The interesting first-order-like properties of the model, reported by Hernández and Diep [34] and Hernández and Ceva [35] for the bimodal RFIM and by Wu and Machta [28] for the Gaussian RFIM, have added more complication and novelty to the RFIM. The first-order-like characteristics of the Gaussian RFIM found by Wu and Machta [28] revealed that the appearance of these strong finite-size effects are independent of the RF distribution and their existence is related to the value of the disorder strength.…”
Section: Revisiting the Order Of The Transition By The High-level Onementioning
confidence: 95%
“…In particular first-order-like features, such as the appearance of the characteristic double-peak (dp) structure of the canonical energy probability density function (PDF), have been recently reported for both the Gaussian and the bimodal distributions of the 3D RFIM. Particularly, Wu and Machta [28], using the Wang-Landau (WL) approach [39,40,41], reported such properties for the Gaussian RFIM at a strong disorder strength value h = 2 below their critical randomness (h c = 2.282). Moreover, Hernández and Diep [34] have emphasized that they have found evidence for the existence of a TCP in the phase diagram of the bimodal RFIM, in agreement with the early predictions of mean-field theory [33].…”
Section: Introductionmentioning
confidence: 99%
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“…This also shows that for each disorder configuration the staggered magnetization changes discontinuously at W c . Such discontinous jumps for bond energy were also reported for 3d RFIM [18,22,34]. The domains of the metastable state in the COP and the domains in ground state of disordered phase are plotted in figure 4 for L=48.…”
Section: Resultsmentioning
confidence: 80%
“…This question remains unclear even for 3d RFIM where there is no controversy over the presence of phase transition at zero temperature. Some earlier work suggested a first order transition [12][13][14][15][16][17][18] but there are arguments [19][20][21][22] which favour second order …”
mentioning
confidence: 99%