Finite-size scaling in Villain's fully frustrated model and singular effects of plaquette disorder

Lukic, J.; Marinari, Enzo; Martin, O. C.

doi:10.1209/epl/i2006-10001-5

Cited by 8 publications

(24 citation statements)

References 12 publications

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“…The A and B values practically agree with Ref. [31]; the crossover temperatures are near T * (L) ≈ 0.5. The present figure can be compared directly to the equivalent figure for the 2D bimodal ISG, Ref.…”

Section: Acknowledgmentssupporting

confidence: 88%

“…[19,31]), an "anti-diluted" bimodal model where a fraction p = 0.2 of the interactions are set randomly to strength ±2J and the remaining fraction to ±J. Also we test a more complex symmetric Poisson model with an interaction distribution shown in Fig.…”

Section: Discrete Interaction Distribution Isgsmentioning

confidence: 99%

“…temperature thermodynamic limit second moment correlation length ξ(β) ∼ exp(2β)/2 [27,31,39]. The FF specific heats in the infinite L and finite L limits were estimated in Ref.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…The FF specific heats in the infinite L and finite L limits were estimated in Ref. [31] by sophisticated Pfaffian algebra to be of the form C v ∼ β B exp(−Aβ), the values being B = 3 in the infinite L limit and B = 2 in the finite L limit with A = 4 in both limits. We show in Fig.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…For the FF model a number of properties have been established analytically [39], by precise energy measurements [31], and by simulations [27]. The FF ground state degeneracy corresponds to a zero temperature entropy per site of 0.2916 [39].…”

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confidence: 99%

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Ising spin glasses in two dimensions: Universality and nonuniversality

Lundow

Campbell

2017

Phys. Rev. E

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Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising Spin Glass (ISG) models in dimension two (P.H. Lundow and I.A. Campbell, Phys. Rev. E 93, 022119 (2016)). Here we further analyse the bimodal and Gaussian data together with data on two other continuous interaction distribution 2D ISG models, the uniform and the Laplacian models, and three other discrete interaction distribution models, a diluted bimodal model, an "anti-diluted" model, and a more exotic symmetric Poisson model. Comparisons between the three continuous distribution models show that not only do they share the same exponent η ≡ 0 but that to within the present numerical precision they share the same critical exponent ν also, and so lie in a single universality class. On the other hand the critical exponents of the four discrete distribution models are not the same as those of the continuous distributions, and differ from one discrete distribution model to another. Discrete distribution ISG models in dimension two have non-zero values of the critical exponent η; they do not lie in a single universality class.

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Section: Acknowledgmentssupporting

confidence: 88%

Section: Discrete Interaction Distribution Isgsmentioning

confidence: 99%

“…temperature thermodynamic limit second moment correlation length ξ(β) ∼ exp(2β)/2 [27,31,39]. The FF specific heats in the infinite L and finite L limits were estimated in Ref.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Section: Acknowledgmentsmentioning

confidence: 99%

mentioning

confidence: 99%

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Ising spin glasses in two dimensions: Universality and nonuniversality

Lundow

Campbell

2017

Phys. Rev. E

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Energy gap of the bimodal two-dimensional Ising spin glass

Poulter

2008

New J. Phys.

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An exact algorithm is used to compute the degeneracies of the excited states of the bimodal Ising spin glass in two dimensions. It is found that the specific heat at arbitrary low temperature is not a self-averaging quantity and has a distribution that is neither normal or lognormal. Nevertheless, it is possible to estimate the most likely value and this is found to scale as L 3 T −2 exp(−4J/kT ), for a L × L lattice. Our analysis also explains, for the first time, why a correlation length ξ ∼ exp(2J/kT ) is consistent with an energy gap of 2J. Our method allows us to obtain results for up to 10 5 disorder realizations with L ≤ 64. Distributions of second and third excitations are also shown.

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Excitations of the bimodal Ising spin glass on the brickwork lattice

Poulter

2009

New J. Phys.

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An exact algorithm is used to investigate the distributions of the degeneracies of low-energy excited states for the bimodal Ising spin glass on the brickwork lattice. Since the distributions are extreme and do not self-average, we base our conclusions on the most likely values of the degeneracies. Our main result is that the degeneracy of the first excited state per ground state and per spin is finite in the thermodynamic limit. This is very different from the same model on a square lattice where a divergence proportional to the linear lattice size is expected. The energy gap for the brickwork lattice is obviously 2J on finite systems and predicted to be the same in the thermodynamic limit. Our results suggest that a 2J gap is universal for planar bimodal Ising spin glasses. The distribution of the second contribution to the internal energy has a mode close to zero and we predict that the low-temperature specific heat is dominated by the leading term proportional to T −2 exp(−2J/kT ).

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Finite-size scaling in Villain's fully frustrated model and singular effects of plaquette disorder

Cited by 8 publications

References 12 publications

Ising spin glasses in two dimensions: Universality and nonuniversality

Ising spin glasses in two dimensions: Universality and nonuniversality

Energy gap of the bimodal two-dimensional Ising spin glass

Excitations of the bimodal Ising spin glass on the brickwork lattice

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