Spin and chirality autocorrelation functions of a Heisenberg spin-glass model

Matsubara, Fumitaka; Shirakura, Takayuki; Endoh, Shin-ichi

doi:10.1103/physrevb.64.092412

Cited by 51 publications

(64 citation statements)

References 25 publications

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“…Therefore, a single phase transition is present in this problem: spin-chirality decoupling is ruled out. We observe logarithmic corrections to scaling, explaining why previous investigations [9,10,11,12,13,14,15,16,17] were inconclusive. Our results are compatible with Kosterlitz-Thouless scaling, but they are typical as well of a system with a lower critical dimension barely smaller than three.…”

supporting

confidence: 63%

“…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]).…”

mentioning

confidence: 99%

“…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]).…”

mentioning

confidence: 99%

“…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).…”

mentioning

confidence: 99%

“…As for ξ L,SG , we treat it here as an observable scaling as L φ . Some groups [15,16,17] expect φ = 1, while others [13,14] believe that φ = 0.…”

mentioning

confidence: 99%

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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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supporting

confidence: 63%

mentioning

confidence: 99%

“…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]).…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…As for ξ L,SG , we treat it here as an observable scaling as L φ . Some groups [15,16,17] expect φ = 1, while others [13,14] believe that φ = 0.…”

mentioning

confidence: 99%

See 3 more Smart Citations

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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Weak Universality of Spin Glasses in Three Dimensions

Nakamura

Endoh

Yamamoto

2004

Springer Proceedings in Physics

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Summary. We point out a possibility of the weak universality of spin-glass phase transitions in three dimensions. The Ising, the XY, and the Heisenberg models with ±J bond distributions undergo finite-temperature phase transitions with a ratio of critical exponents γ/ν = 2.4. Evaluated critical exponents agree with corresponding experimental results. The analyses are based upon the nonequilibrium relaxation from the paramagnetic state and the finite-time scaling.

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Some recent developments in spin glasses

Young

2005

Pramana - J Phys

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Spin and chirality autocorrelation functions of a Heisenberg spin-glass model

Cited by 51 publications

References 25 publications

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

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

Weak Universality of Spin Glasses in Three Dimensions

Some recent developments in spin glasses

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