Specific Heat Singularity in Two-Dimensional Random Ising Ferromagnets

Stauffer, Dietrich; Reis, F. D. A. Aarão; Queiroz, S. L. A. de; Santos, Raimundo R. dos

doi:10.1142/s0129183197001077

Cited by 19 publications

(38 citation statements)

References 12 publications

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“…Our purpose was twofold: first we wanted to address again the question about the reliability of the method; second, we extended the study started in Ref. 21 to systems of larger sizes, also in view of the new results which have appeared in the literature since then, [12][13][14][15][16] in order to allow perhaps a clearer discrimination between the two contradicting pictures of the system's critical behaviour that survived so far, the logarithmic corrections and the weak universality scenario.…”

Section: Discussionmentioning

confidence: 99%

“…(13)) to the anomalous dimension of the spin-spin correlation function via A = πη, providing a simple method to extract η just by extrapolating the sequence L/ξ L to L → ∞. The same procedure can be applied as well to Lβσ L since the amplitudes for the correlation length and for the wall free energy are equal.…”

Section: B the Exponent η And The Ratio γ/νmentioning

confidence: 99%

“…We plot our data for the specific heat in the same form as in Ref. 13, i.e. against both ln L and ln ln L (Fig.…”

Section: E the Specific Heatmentioning

confidence: 99%

“…These models have been widely studied, both because the corresponding pure system is well understood and because they constitute a marginal case in the Harris criterion 1 which assesses whether disorder constitutes a relevant or irrelevant perturbation for the critical behaviour of the pure system. For models of this type, the discussion currently appears to narrow down on two conflicting scenarios, namely the logarithmic corrections [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] versus the weak universality [18][19][20][21] scenario, though a broader spectrum of alternatives had been discussed earlier [22][23][24] (the interested reader will find a comprehensive report on the literature up to approximately 1982 in an early review by Stinchcombe 25 ). We will describe these scenarios and discuss these (and related) results in greater detail later on.…”

Section: Introductionmentioning

confidence: 99%

“…with the same critical exponents) as that of the pure 2d Ising model. These findings are almost all concerned with the ferromagnetic bond disordered situation, either theoretically, [3][4][5]17 or via numerical 6,7,[9][10][11][12][13][14]16 and series expansion 15 approaches, but the comparison with the spin diluted model is possible supposing -as it is generally believed to be the case -that the two systems are in the same universality class. 25,17 In discussing our results, we have to address two main issues.…”

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confidence: 99%

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Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach

Mazzeo

Kühn

1999

Phys. Rev. E

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The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to put the equilibrium ensemble approach to work. A new method to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open in both directions. A critical discussion shows that, still, an unambiguous discrimination between the two scenarios is not possible on the basis of the available finite size data.

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Section: Discussionmentioning

confidence: 99%

Section: B the Exponent η And The Ratio γ/νmentioning

confidence: 99%

“…We plot our data for the specific heat in the same form as in Ref. 13, i.e. against both ln L and ln ln L (Fig.…”

Section: E the Specific Heatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach

Mazzeo

Kühn

1999

Phys. Rev. E

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Monte Carlo analysis of critical properties of the two-dimensional randomly site-diluted Ising model via Wang–Landau algorithm

Hadjiagapiou

Malakis

Martinos

2008

Physica A: Statistical Mechanics and its Applications

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The influence of random site dilution on the critical properties of the two-dimensional Ising model on a square lattice was explored by Monte Carlo simulations with the Wang-Landau sampling. The lattice linear size was L = 20 − 120 and the concentration of diluted sites q = 0.1, 0.2, 0.3. Its pure version displays a second-order phase transition with a vanishing specific heat critical exponent α, thus, the Harris criterion is inconclusive, in that disorder is a relevant or irrelevant perturbation for the critical behavior of the pure system. The main effort was focused on the specific heat and magnetic susceptibility. We have also looked at the probability distribution of susceptibility, pseudocritical temperatures and specific heat for assessing self-averaging. The study was carried out in appropriate restricted but dominant energy subspaces. By applying the finite-size scaling analysis, the correlation length exponent ν was found to be greater than one, whereas the ratio of the critical exponents (α/ν) is negative and (γ/ν) retains its pure Ising model value supporting weak universality.

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Spin models on random lattices

Janke¹,

Johnston²,

Villanova³

2000

Physica A: Statistical Mechanics and its Applications

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Under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a di erent behaviour than in the corresponding pure system. Here we discuss a series of Monte Carlo studies of a special type of such disordered systems, namely spin models deÿned on quenched, random lattices exhibiting geometrical disorder in the connectivity of the lattice sites. In two dimensions we present results for the q-state Potts model on random tri-valent ( 3 ) planar graphs, which appear quite naturally in the dynamically triangulated random surface (DTRS) approach to quantum gravity, as well as on Poissonian random lattices of Voronoi=Delaunay type. Both cases, q64 and ¿ 4, are discussed which, in the pure model without disorder, give rise to second-and ÿrst-order phase transitions, respectively. In three dimensions results for the Ising model on Poissonian random lattices are brie y described. We conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder, and a discussion of the distinguishing di erences.

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Specific Heat Singularity in Two-Dimensional Random Ising Ferromagnets

Cited by 19 publications

References 12 publications

Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach

Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach

Monte Carlo analysis of critical properties of the two-dimensional randomly site-diluted Ising model via Wang–Landau algorithm

Spin models on random lattices

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