Universality in three-dimensional Ising spin glasses: A Monte Carlo study

Katzgraber, Helmut G.; Körner, Mathias; Young, A. P.

doi:10.1103/physrevb.73.224432

Cited by 216 publications

(381 citation statements)

References 41 publications

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“…Palassini and Caracciolo [3]. These works demonstrated the applicability to spin-glasses of our approach [4,5] to Finite Size Scaling (FSS) at the critical temperature, as well as that of Caracciolo and coworkers [6] for the paramagnetic state (see also [7,8]). …”

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confidence: 85%

Spin-Glass Transition of the Three-Dimensional Heisenberg Spin Glass

Campos¹,

Cotallo-Abán

Martı́n-Mayor

et al. 2006

Phys. Rev. Lett.

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It is shown, by means of Monte Carlo simulation and Finite Size Scaling analysis, that the Heisenberg spin glass undergoes a finite-temperature phase transition in three dimensions. There is a single critical temperature, at which both a spin glass and a chiral glass orderings develop. The Monte Carlo algorithm, adapted from lattice gauge theory simulations, makes possible to thermalize lattices of size L = 32, larger than in any previous spin glass simulation in three dimensions. High accuracy is reached thanks to the use of the Marenostrum supercomputer. The large range of system sizes studied allow us to consider scaling corrections. Palassini and Caracciolo [3]. These works demonstrated the applicability to spin-glasses of our approach [4,5] to Finite Size Scaling (FSS) at the critical temperature, as well as that of Caracciolo and coworkers [6] for the paramagnetic state (see also [7,8]).However, the situation is still confusing for Heisenberg spin glasses [9,10,11,12,13,14,15,16,17], which is the more experimentally interesting case (see e.g. [18,19]). Indeed, numerical studies are the only theoretical tool to achieve progress in three dimensions. Early simulations [9] could not reach low enough temperatures due to the dramatic dynamical arrest of the algorithms available at the time, and concluded that the critical temperature, T c , was strictly zero. Yet, recent studies at lower temperatures [16,17] found indirect indications of a spin glass transition for Heisenberg spin glasses. Matters are further complicated by the Villain et al. [12] suggestion of a low temperature chiral glass phase, with an Ising like ordering due to the handedness of the non-collinear spin structures (see definitions below). The simulations of Kawamura and coworkers [13,14] gave ample support to this spin-chirality decoupling scenario (i.e. T c = 0 for the spin glass, but T c > 0 for the chiral glass ordering).In order to clarify the situation for Heisenberg and XY spin glasses in D = 3, Young and Lee [15] have recently tried our FSS methods at T c [2,4]. Although parallel tempering only allowed them [15] to thermalize systems of size up to L = 12, very clear results were reached for the XY spin glasses. The finite-lattice correlation length [20], ξ L , was analyzed for several system sizes L. As expected [2,4,5], the dimensionless ratio ξ L /L crosses neatly at the same T c , for the chiral glass and the spin glass ordering, for XY spin glasses. In the more important case of Heisenberg spin glasses, their results, although inconclusive, were interpreted also as lack of spin-chirality decoupling. This conclusion has been criticized by Kawamura and Hukushima [14], that studied somehow larger systems on very few samples.Here we show that a finite-temperature spin glass transition occurs for the Heisenberg spin glass in D = 3. The critical temperature for the spin glass transition coincides with that of the chiral glass. Our results rely on Monte Carlo simulation and FSS analysis at T c [2,4,5]. We adapt a lattice gauge theory alg...

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mentioning

confidence: 85%

Spin-Glass Transition of the Three-Dimensional Heisenberg Spin Glass

Campos¹,

Cotallo-Abán

Martı́n-Mayor

et al. 2006

Phys. Rev. Lett.

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“…Over the years many estimates of the critical exponents have been obtained. 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.…”

Section: Introductionmentioning

confidence: 99%

“…to belong to a universality class which is independent of the details of the model and, in particular, of the disorder distribution. Several numerical works 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33 have addressed these issues, considering various Ising spin-glass models, characterized by different disorder distributions, with or without dilution. Over the years many estimates of the critical exponents have been obtained.…”

Section: Introductionmentioning

confidence: 99%

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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“…Here we use 20 inverse temperatures equally spaced between β = 0.16 to β = 0.92. The phase transition temperature of the system was recently measured as β c = 0.89 ± 0.03 [32]. A single sweep of the full algorithm consists of a CMR cluster sweep for each pair of replicas at each temperature, a parallel tempering exchange between replicas at each pair of neighboring temperatures and a Metropolis sweep for every replica.…”

Section: Numerical Methods and Resultsmentioning

confidence: 99%

“…For the threedimensional Ising spin glass on the cubic lattice, Fortuin-Kasteleyn bonds percolate at β FK,p ≈ 0.26 [31] while the inverse critical temperature is believed to be β c = 0.89 ± 0.03 [32]. Near the spin glass critical temperature, the giant FK cluster includes most of the sites of the system.…”

Section: B Spin Glass Models; the Trfk Representationmentioning

confidence: 99%

A Percolation-theoretic Approach to Spin Glass Phase Transitions

Machta

Newman

Stein

2009

Progress in Probability

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The magnetically ordered, low temperature phase of Ising ferro-magnets is manifested within the associated Fortuin-Kasteleyn (FK) random cluster representation by the occurrence of a single positive density percolating cluster. In this paper, we review our recent work on the percolation signature for Ising spin glass ordering -both in the short-range Edwards-Anderson (EA) and infinite-range Sherrington-Kirkpatrick (SK) models -within a two-replica FK representation and also in the different Chayes-Machta-Redner two-replica graphical representation. Numerical studies of the ±J EA model in dimension three and rigorous results for the SK model are consistent in supporting the conclusion that the signature of spin-glass order in these models is the existence of a single percolating cluster of maximal density normally coexisting with a second percolating cluster of lower density.

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Universality in three-dimensional Ising spin glasses: A Monte Carlo study

Cited by 216 publications

References 41 publications

Spin-Glass Transition of the Three-Dimensional Heisenberg Spin Glass

Spin-Glass Transition of the Three-Dimensional Heisenberg Spin Glass

Critical behavior of three-dimensional Ising spin glass models

A Percolation-theoretic Approach to Spin Glass Phase Transitions

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