The critical exponents of the two-dimensional Ising spin glass revisited: Exact ground-state calculations and Monte Carlo simulations

Rieger, Heiko; Santen, Ludger; Blasum, Ulrich; Diehl, M.; Jünger, Michael

doi:10.1088/0305-4470/30/24/038

Cited by 19 publications

(15 citation statements)

References 12 publications

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“…This suggests that the correlation length diverges at zero temperature quite similar to the statics of the two-dimensional Ising spin-glass model studied by Young 34 and more recently revisited by Rieger and collaborators. 35 Similarly to that case, in our model the growth of the correlation length is quite small compared to the growth of the correlation time with the temperature, which is also super-Arrhenius. In fact, a fit of the relaxation time obtained in Eq.…”

Section: Thermodynamicssupporting

confidence: 67%

Fragile-glass behavior of a short-rangep-spin model

1996

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We propose a short-range generalization of the p-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We, however, encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin-glass susceptibility, investigating the behavior of the correlation length in the system. We find that the increase of the relaxation time is accompanied by a very slow growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory. ͓S0163-1829͑96͒04137-9͔

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Section: Thermodynamicssupporting

confidence: 67%

Fragile-glass behavior of a short-rangep-spin model

1996

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“…18,19,20,21,22,23,24,25 The energy of the domain wall is found to vary as L θ where L is the system size and θ is positive (for systems with T c > 0). The droplet theory assumes that the stiffness exponent for domain walls θ domain−wall is the same as the stiffness exponent for dropletlike excitations θ droplet .…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions

2003

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We present results from Monte Carlo simulations of the one-dimensional Ising spin glass with power-law interactions at low temperature, using the parallel tempering Monte Carlo method. For a set of parameters where the long-range part of the interaction is relevant, we find evidence for large-scale dropletlike excitations with an energy that is independent of system size, consistent with replica symmetry breaking. We also perform zero-temperature defect energy calculations for a range of parameters and find a stiffness exponent for domain walls in reasonable but by no means perfect agreement with analytic predictions.

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“…For the Gaussian ISG, θ = −0.282(2). 10,13 From the scaling rules applied at a zero temperature transition, 14,15 we obtain for the critical exponent ν = −1/θ, hence ν = 3.55(3). 15,16 For the ±J 2d ISG, large-L simulations 10 on samples with periodic/antiperiodic boundary conditions along one axis and free boundary conditions on the other axis showed θ = 0, with significant corrections to scaling up to L ∼ 100.…”

Section: Introductionmentioning

confidence: 99%

Energy size effects of two-dimensional Ising spin glasses

2004

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We analyze exact ground-state energies of two-dimensional Ising spin glasses with either Gaussian or bimodal nearest-neighbor interactions for large system sizes and for three types of boundary conditions: free on both axes, periodic on both axes, and free on one axis and periodic on the other. We find accurate values for bulk-, edge-, and corner-site energies. Fits for the system with Gaussian bonds are excellent for all types of boundary conditions over the whole range of system sizes. In particular, the leading behavior for nonfree boundary conditions is governed by the stiffness exponent θ ≈ −0.282 describing the scaling of domain-wall and droplet excitations. For the system with a bimodal distribution of bonds the fit is good for free boundary conditions but worse for other geometries, particularly for periodic-free boundary conditions where there appear to be unorthodox corrections to scaling up to large sizes. Finally, by introducing hard bonds we test explicitly for the Gaussian case the relationship between domain walls and the standard scaling behavior.

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The critical exponents of the two-dimensional Ising spin glass revisited: Exact ground-state calculations and Monte Carlo simulations

Cited by 19 publications

References 12 publications

Fragile-glass behavior of a short-rangep-spin model

Fragile-glass behavior of a short-rangep-spin model

Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions

Energy size effects of two-dimensional Ising spin glasses

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