Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Liers, Frauke; Lukic, J.; Marinari, Enzo; Pelissetto, Andrea; Vicari, Ettore

doi:10.1103/physrevb.76.174423

Cited by 14 publications

(11 citation statements)

References 45 publications

(57 reference statements)

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“…Accurate determinations of θ are available for the Gaussian model: −θ = 0.281(2) [22], 0.282(2) [24], 0.282(3) [25], and 0.282(4) [26]. A computation for the random anisotropy model yields θ = 0.275(5) [30]. We shall obtain results of comparable accuracy for 1/ν.…”

Section: The Thermal Exponentmentioning

confidence: 77%

Universal critical behavior of the two-dimensional Ising spin glass

et al. 2016

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We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.

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Section: The Thermal Exponentmentioning

confidence: 77%

Universal critical behavior of the two-dimensional Ising spin glass

et al. 2016

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“…There is a substantial agreement, which confirms that the critical behavior of the random-anisotropy Heisenberg model for infinite anisotropy belongs to the Ising spin-glass universality class. 27,35 …”

Section: The Zero-momentum Quartic Couplings G 4 and G 22 In Thmentioning

confidence: 99%

“…If we now substitute relation (40) into Eqs. (29), (30), (31), and (32), we obtain the expansion of the different quantities at fixed R f , which we denote by adding a bar: given (34), (35), and (36), with different coefficients, of course. If R f = R * , we must be more careful.…”

Section: Finite-size Scalingmentioning

confidence: 99%

“…We mention the most recent ones for the correlation-length exponent ν: ν = 2.39(5), 30 ν = 2.72(8), 29 ν = 1.5(3), 23 ν = 1.35(10), 22 ν = 2.15 (15), 21 ν = 1.8(2), 20 obtained from simulations of the symmetric model with bimodal distribution; ν = 2.22 (15) for the bond-diluted symmetric bimodal model with p b = 0.45; 28 ν = 2.44(9) 30 and ν = 2.00 (15) 18 for the symmetric model with Gaussian disorder distribution; ν = 2.4 (6) for the random-anisotropy Heisenberg model in the limit of large anisotropy, 27 which is expected to be in the same Ising spin-glass universality class. 27,34,35 Moreover, the analysis of different quantities has often given different estimates of the same critical exponent, even in the same model. For instance, recent Monte Carlo (MC) studies 29,30 find significant discrepancies among the estimates of the exponent ν obtained from the finite-size scaling (FSS) at T c of the temperature derivative of ξ/L, of the Binder cumulant, and of the overlap susceptibility.…”

Section: Introductionmentioning

confidence: 99%

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Critical behavior of three-dimensional Ising spin glass models

Pelissetto²,

2008

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We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin-glass models on cubic lattices of size L: the ±J (Edwards-Anderson) Ising model for two values of the disorder parameter p, p = 0.5 and p = 0.7 (up to L = 28 and L = 20, respectively), and the bond-diluted bimodal model for bond-occupation probability p b = 0.45 (up to L = 16). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent ω related to the leading irrelevant operator: ω = 1.0(1). Shorter Monte Carlo simulations of the bond-diluted bimodal models at p b = 0.7 and p b = 0.35 (up to L = 10) and of the Ising spinglass model with Gaussian bond distribution (up to L = 8) also support the existence of a unique Ising spin-glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents ν and η: we obtain ν = 2.45(15) and η = −0.375(10).

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“…The web-based Spin Glass Server [4] is especially designed for fast solutions of instances defined on grids that arise in statistical physics [39]. For instance, for a two-dimensional lattice with L ≤ 80 and periodic boundary conditions, one ground-state computation takes less than two minutes on average on a SUN Opteron (2.2 GHz) machine; for 120 2 lattices the computation takes 28 minutes [40]. On the other hand, SDP-based methods perform better for dense instances of max-cut [46].…”

Section: Introductionmentioning

confidence: 99%

Solving k-Way Graph Partitioning Problems to Optimality: The Impact of Semidefinite Relaxations and the Bundle Method

Anjos

Ghaddar²,

Hupp

et al. 2013

Facets of Combinatorial Optimization

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This paper is concerned with computing global optimal solutions for maximum k-cut problems. We improve on the SBC algorithm of Ghaddar, Anjos and Liers in order to compute such solutions in less time. We extend the design principles of the successful BiqMac solver for maximum 2-cut to the general maximum k-cut problem. As part of this extension, we investigate different ways of choosing variables for branching. We also study the impact of the separation of clique inequalities within this new framework and observe that it frequently reduces the number of subproblems considerably. Our computational results suggest that the proposed approach achieves a drastic speedup in comparison to SBC, especially when k = 3. We also made a comparison with the orbitopal fixing approach of Kaibel, Peinhardt and Pfetsch. The results suggest that while their performance is better for sparse instances and larger values of k, our proposed approach is superior for smaller k and for dense instances of medium size. Furthermore, we used CPLEX for solv- ing the ILP formulation underlying the orbitopal fixing algorithm and conclude that especially on dense instances the new algorithm outperforms CPLEX by far.

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Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Cited by 14 publications

References 45 publications

Universal critical behavior of the two-dimensional Ising spin glass

Universal critical behavior of the two-dimensional Ising spin glass

Critical behavior of three-dimensional Ising spin glass models

Solving k-Way Graph Partitioning Problems to Optimality: The Impact of Semidefinite Relaxations and the Bundle Method

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