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. At positive temperature the specific heat and the susceptibility are obtained using the Wang-Landau algorithm. It is found that sharp peaks are present in these physical quantities for some realizations of systems sized 16 3 and larger. These sharp peaks result from flipping large domains and correspond to large discontinuities in ground state bond energies. Finally, zero temperature and positive temperature spin configurations near the critical line are found to be highly correlated suggesting a strong version of the zero temperature fixed point hypothesis.

First-order transition features of the 3D bimodal random-field Ising model

“…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.…”

“…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].…”

“…Finally, we summarize our conclusions in section 3. Several sophisticated simulation techniques, such as cluster algorithms and flathistogram approaches, have been used to study the RFIM [11,24,34,35,56,57,58,59], while graph theoretical algorithms have been used to study properties of the groundstates of this model [14,20,21,22,23,25,26,28,60]. Entropic sampling methods such as the Lee [61,62] and WL [39,40,41] methods are efficient alternatives for complex systems and systems that undergo first-order transitions.…”

First order transition in two dimensional coulomb glass

“…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.…”

“…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 …”