Evidence for Two Exponent Scaling in the Random Field Ising Model

Gofman, Misha; Adler, Joan; Aharony, Amnon; Harris, Amanda; Schwartz, Moshe

doi:10.1103/physrevlett.71.2841.2

Cited by 17 publications

(4 citation statements)

References 5 publications

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“…This is a further strong manifestation in favor of the continuous phase transition scenario. Thus, the evidence presented in this subsection for the 3D bimodal RFIM is in agreement with the favored view of most existing theoretical and numerical studies [17,19,54,57] that the phase transition of the 3D RFIM is of second order. In order to present even stronger numerical evidence of a vanishing (in the limit L → ∞) surface tension we will now attempt to go well beyond the observation of several typical RF realizations.…”

Section: One-r Wl Approach Transition Identification By the Lk Methodssupporting

confidence: 91%

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

2008

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Abstract. Two numerical strategies based on the Wang-Landau and Lee entropic sampling schemes are implemented to investigate the first-order transition features of the 3D bimodal (±h) random-field Ising model at the strong disorder regime. We consider simple cubic lattices with linear sizes in the range L = 4 − 32 and simulate the system for two values of the disorder strength: h = 2 and h = 2.25. The nature of the transition is elucidated by applying the Lee-Kosterlitz free-energy barrier method. Our results indicate that, despite the strong first-order-like characteristics, the transition remains continuous, in disagreement with the early mean-field theory prediction of a tricritical point at high values of the random-field.

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Section: One-r Wl Approach Transition Identification By the Lk Methodssupporting

confidence: 91%

“…Various RF probability distributions, such as the Gaussian, the wide bimodal distribution (with a Gaussian width), and the above bimodal distribution have been considered [17,18,19,20,21,22,23,24,25,26,27,28,29].…”

Section: Introductionmentioning

confidence: 99%

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

2008

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“…The ground state of the RFIM can be found in polynomial time 13 by efficient combinatorial algorithms so that zero temperature simulations are much faster and allow for much larger system sizes than positive temperature simulations. Critical exponents have been obtained from zero temperature studies 14,15,16 that are mostly consistent with the scaling theories 5,6,7 , series methods 17 and real space renormalization group approaches 18,19,20 .…”

Section: Introductionmentioning

confidence: 95%

Numerical study of the three-dimensional random-field Ising model at zero and positive temperature

Machta

2006

Phys. Rev. B

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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.

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“…Ground states are much easier to simulate than thermal states and, according to the zero temperature fixed point hypothesis, the T = 0 and T > 0 transitions are in the same universality class. Critical exponents have been obtained from zero temperature studies that are mostly consistent with the scaling theories [5,6,7], series methods [16] and real space renormalization group approaches [17,18,19].…”

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confidence: 99%

Ground States and Thermal States of the Random Field Ising Model

Wu¹,

Machta²

2005

Phys. Rev. Lett.

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The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random field and external field strength. Thermal states and thermodynamic properties are obtained for all temperatures using the Wang-Landau algorithm. The specific heat and susceptibility typically display sharp peaks in the critical region for large systems and strong disorder. These sharp peaks result from large domains flipping. For a given realization of disorder, ground states and thermal states near the critical line are found to be strongly correlated--a concrete manifestation of the zero temperature fixed point scenario.

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Evidence for Two Exponent Scaling in the Random Field Ising Model

Cited by 17 publications

References 5 publications

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

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

Numerical study of the three-dimensional random-field Ising model at zero and positive temperature

Ground States and Thermal States of the Random Field Ising Model

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