Gauge-invariant method for the ±<i>J</i>spin-glass model

Blackman, J. A.; Poulter, J.

doi:10.1103/physrevb.44.4374

Cited by 35 publications

(61 citation statements)

References 35 publications

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“…While we have not studied these questions in detail, there are certainly situations where this does indeed happen. Thus, in the particular fermionic ImRH representation 42 of the two-dimensional random bond Ising model, our preliminary results suggest that the density of states is power-law vanishing to the left ͑the lessdisordered side͒ of the Nishimori line and power-law diverging to the right ͑this particular example was suggested to us by Nick Read and the corresponding result proved for a onedimensional toy model in Ref. 43͒.…”

Section: Discussionmentioning

confidence: 87%

Particle-hole symmetric localization in two dimensions

2002

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We revisit two-dimensional particle-hole symmetric sublattice localization problem, focusing on the origin of the observed singularities in the density of states (E) at the band center Eϭ0. The most general system of this kind ͓R. Gade, Nucl. Phys. B 398, 499 ͑1993͔͒ exhibits critical behavior and has (E) that diverges stronger than any integrable power law, while the special random vector potential model of Ludwig et al. ͓Phys. Rev. B 50, 7526 ͑1994͔͒ has instead a power-law density of states with a continuously varying dynamical exponent. We show that the latter model undergoes a dynamical transition with increasing disorder-this transition is a counterpart of the static transition known to occur in this system; in the strong-disorder regime, we identify the low-energy states of this model with the local extrema of the defining two-dimensional Gaussian random surface. Furthermore, combining this ''surface fluctuation'' mechanism with a renormalization group treatment of a related vortex glass problem leads us to argue that the asymptotic low-E behavior of the density of states in the general case is (E)ϳE Ϫ1 e Ϫc͉ln E͉ 2/3 , different from earlier prediction of Gade. We also study the localized phases of such particle-hole symmetric systems and identify a Griffiths ''string'' mechanism that generates singular power-law contributions to the low-energy density of states in this case.

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Section: Discussionmentioning

confidence: 87%

Particle-hole symmetric localization in two dimensions

2002

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“…From the log-log plots in Figs. 2(a) and 3(a), we find that b is proportional to L 1.78 (2) and L 1.81(4) , respectively, while from Figs. 8(a) and 9(a), the scaling of −A is essentially indistinguishable from L 2 .…”

Section: Ground State Propertiesmentioning

confidence: 87%

“…In recent years it has become possible to compute the free energy of the two-dimensional (2D) Ising spin glass with ±J bonds on L × L lattices with L of 100 or more. 2,3,4,5,6,7 From these calculations on large lattices we have learned that extrapolations of data from lattices with L < 30 are often misleading. 8,9,10,11,12 A better understanding of why this happens is clearly desirable.…”

Section: Introductionmentioning

confidence: 99%

“…A fit to the data gives the result that each additional broken bond in the ground state of a particular sample of random bonds increases the ground state degeneracy by approximately a factor of 10/3. For x = 0.5 (where x is the fraction of negative bonds), over this range of L, the characteristic entropy defined by the energy-entropy correlation scales with size as L 1.78 (2) . Anomalous scaling is not found for the characteristic energy, which essentially scales as L 2 .…”

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confidence: 99%

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Finite-Size Scaling in the Energy-Entropy Plane for the 2D ± Ising Spin Glass

Fisch¹

2006

J Stat Phys

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For L × L square lattices with L ≤ 20 the 2D Ising spin glass with +1 and -1 bonds is found to have a strong correlation between the energy and the entropy of its ground states. A fit to the data gives the result that each additional broken bond in the ground state of a particular sample of random bonds increases the ground state degeneracy by approximately a factor of 10/3. For x = 0.5 (where x is the fraction of negative bonds), over this range of L, the characteristic entropy defined by the energy-entropy correlation scales with size as L 1.78(2) . Anomalous scaling is not found for the characteristic energy, which essentially scales as L 2 . When x = 0.25, a crossover to L 2 scaling of the entropy is seen near L = 12. The results found here suggest a natural mechanism for the unusual behavior of the low temperature specific heat of this model, and illustrate the dangers of extrapolating from small L.

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“…A large class of models possess a "Nishimori line" in their phase diagram, on which the internal energy is analytic [2], and the correlation functions of the Ising spins obey certain identities [2,3]. In two dimensions, the Ising model can be represented as a noninteracting fermion problem, even when the bonds are random [4]. The problem then reduces to something similar to a two-dimensional (2D) tight-binding Hamiltonian with quenched disorder.…”

Section: Introductionmentioning

confidence: 99%

Absence of a metallic phase in random-bond Ising models in two dimensions: Applications to disordered superconductors and paired quantum Hall states

Read

Ludwig

2000

Phys. Rev. B

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When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma model analysis of the latter in two dimensions has previously led to the prediction of a metallic phase, in which the fermion eigenstates at zero energy are extended. In this paper we argue that such behavior cannot occur in the random-bond Ising model, by showing that the Ising spin correlations in the metallic phase violate the bound on such correlations that results from the reality of the Ising couplings. Some types of disorder in spinless or spin-polarized p-wave superconductors and paired fractional quantum Hall states allow a mapping onto an Ising model with real but correlated bonds, and hence a metallic phase is not possible there either. It is further argued that vortex disorder, which is generic in the fractional quantum Hall applications, destroys the ordered or weak-pairing phase, in which nonabelian statistics is obtained in the pure case.

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Gauge-invariant method for the ±Jspin-glass model

Cited by 35 publications

References 35 publications

Particle-hole symmetric localization in two dimensions

Particle-hole symmetric localization in two dimensions

Finite-Size Scaling in the Energy-Entropy Plane for the 2D ± Ising Spin Glass

Absence of a metallic phase in random-bond Ising models in two dimensions: Applications to disordered superconductors and paired quantum Hall states

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