Critical behavior of the specific heat for pure and site-diluted simple cubic Ising systems

Weyersberg, A.; Holey, T.; Fähnle, M.

doi:10.1007/bf01060063

Cited by 4 publications

(6 citation statements)

References 14 publications

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“…Therefore we took into account a background contribution presuming c(T c,d (L), L) = a + bL p with p = α/ν similar to Ref. 39. Moreover, in order to avoid numerical problems, we approximated c(T c,d (L), L) by a + b(L p − 1)/p instead of by a + bL p .…”

Section: Quantitative Analysis By Means Of Finite-size Scalingmentioning

confidence: 99%

Critical behavior of the Coulomb-glass model in the zero-disorder limit: Ising universality in a system with long-range interactions

Möbius

Rößler

2009

Phys. Rev. B

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The ordering of charges on half-filled hypercubic lattices is investigated numerically, where electroneutrality is ensured by background charges. This system is equivalent to the s = 1/2 Ising lattice model with antiferromagnetic 1/r interaction. The temperature dependences of specific heat, mean staggered occupation, and of a generalized susceptibility indicate continuous order-disorder phase transitions at finite temperatures in two-and three-dimensional systems. In contrast, the susceptibility of the one-dimensional system exhibits singular behavior at vanishing temperature. For the two-and three-dimensional cases, the critical exponents are obtained by means of a finite-size scaling analysis. Their values are consistent with those of the Ising model with short-range interaction, and they imply that the studied model cannot belong to any other known universality class. Samples of up to 1400, 112 2 , and 22 3 sites are considered for dimensions 1 to 3, respectively.

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Section: Quantitative Analysis By Means Of Finite-size Scalingmentioning

confidence: 99%

Critical behavior of the Coulomb-glass model in the zero-disorder limit: Ising universality in a system with long-range interactions

Möbius

Rößler

2009

Phys. Rev. B

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“…We are unaware of any previous findings attesting to differences in the asymptotic critical behavior between the two ensembles. Because of the (spatially) uncorrelated nature of the disorder in the grand canonical ensemble it is favored for its relative simplicity by theoretical studies (see [20] for references) and by numerical studies [33][34][35][36][37] aiming to test them. On the other hand, in studying by Monte Carlo average thermodynamic observables, errors can be reduced by using canonical disorder, as was done in [32].…”

Section: A Details Of the Simulationsmentioning

confidence: 99%

“…In addition to calculating the observables m, χ, Γ, a histogram of the energy and magnetization was generated. Using the single histogram reweighting technique [21][22][23][24][25] (For previous studies of disordered systems utilizing the histogram reweighting technique see [36,43]), this histogram can serve to calculate observables at temperatures close to K 1 . By calculating χ at different temperatures a first estimate for the susceptibility maximum χ 1 max and the temperature at which it occurs K 1 max was obtained.…”

Section: Scaling Of Pseudo Critical Temperaturesmentioning

confidence: 99%

“…We are unaware of any previous findings attesting to differences in the asymptotic critical behavior between the two ensembles. Because of the (spatially) uncorrelated nature of the disorder in the grand canonical ensemble it is favored for its relative simplicity by theoretical studies (see [20] for references) and by numerical studies [33][34][35][36][37] TABLE II. Number of site-dilute samples simulated for each model and lattice size l. The last column lists the infinite lattice critical temperature, as estimated by Heuer [32], at which the simulations were performed.…”

Section: A Details Of the Simulationsmentioning

confidence: 99%

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Self-averaging, distribution of pseudocritical temperatures, and finite size scaling in critical disordered systems

1998

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We evaluate by Monte Carlo simulations various singular thermodynamic quantities X, for an ensemble of quenched random Ising and Ashkin-Teller models. The measurements are taken at T c and we study how the distributions P (X) (and, in particular, their relative squared width, R X ) over the ensemble depend on the system size l. The Ashkin-Teller model was studied in the regime where bond randomness is irrelevant and we found weak self averaging; R X ∼ l α ν → 0, where α < 0 and ν are the exponents (of the pure model fixed point) governing the transition. For the site dilute Ising model on a cubic lattice, known to be governed by a random fixed point, we find that R X tends to a universal constant independent of the amount of dilution (no self averaging). However this constant is different for canonical and grand canonical disorder. We identify the pseudo-critical temperatures T c (i, l) of each sample i, as the temperature at which the susceptibility reaches its maximal value. The distribution of these T c (i, l) over the ensemble was investigated; we found that its variance scales as (δT c (l)) 2 ∼ l − 2 ν . These results are in agreement with the recent predictions of Aharony and Harris. Our previously proposed finite size scaling ansatz for disordered systems was tested and found to hold. When we fit the data obtained for many samples of different sizes by a sample-independent form, the resulting scaling function was found to be universal and to behave similarly to pure systems. We did observe that to describe deviations from this universal function we do need sample-dependent scaling functions. These deviations are, however, relatively small and this led us to an interesting side result: sample-to-sample fluctuations of χ max , the susceptibility measured at T c (i, l), are smaller by a factor of 70 than those of χ(T c ). This indicates that to obtain a fixed statistical error it may be more computationally efficient to measure χ max . 05.50.+q, 75.10Nr, 75.40Mg, 75.50.Lk

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“…Theoretical investigations, using approaches based on the renormalization group , and numerical Monte Carlo simulations [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], support the existence of a new random Ising fixed point describing the critical behavior along the T c (x) line: the critical exponents are dilution independent (for sufficiently low dilution) and different from those of the pure Ising model.…”

Section: Introductionmentioning

confidence: 99%

Randomly dilute spin models: A six-loop field-theoretic study

2000

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We consider the Ginzburg-Landau MN model that describes M N-vector cubic models with O(M)-symmetric couplings. We compute the renormalization-group functions to six-loop order in d=3. We focus on the limit N->O which describes the critical behavior of an M-vector model in the presence of weak quenched disorder. We perform for the critical exponents: y=1.330(17), v=0.678(10), eta = 0.030(3), alpha = -0.034(30), Beta = 0.349(5), omega = 0.25(10). For M greater than or equal to 2 we show that the O(M) fixed point is stable, in agreement with general nonperturbative arguments, and that no random fixed point exists

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Critical behavior of the specific heat for pure and site-diluted simple cubic Ising systems

Cited by 4 publications

References 14 publications

Critical behavior of the Coulomb-glass model in the zero-disorder limit: Ising universality in a system with long-range interactions

Critical behavior of the Coulomb-glass model in the zero-disorder limit: Ising universality in a system with long-range interactions

Self-averaging, distribution of pseudocritical temperatures, and finite size scaling in critical disordered systems

Randomly dilute spin models: A six-loop field-theoretic study

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