Stiffness of the Ground-State of a Heisenberg Spin-Glass Model

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

doi:10.1143/jpsj.69.1927

Cited by 33 publications

(48 citation statements)

References 25 publications

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“…In fact, we found that the rotated angles of the spins gradually increase from layer to layer, reminicent of the spin-wave excitation. 21) We note, however, that the coefficient of A ∼ 0.14J is much smaller than that of A = 0.5J in the ferromagnetic model.…”

Section: §2 Model and Methodscontrasting

confidence: 53%

Stiffness of the Heisenberg Spin-Glass Model at Zero- and Finite-Temperatures in Three Dimensions

2001

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We examine the stiffness of the Heisenberg spin-glass (SG) model at both zero temperature (T = 0) and finite temperatures (T = 0) in three dimensions. We calculate the excess energies at T = 0 which are gained by rotating and reversing all the spins on one surface of the lattice, and find that they increase with the lattice size L. We also calculate the excess free-energies at T = 0 which correspond to these excess energies, and find that they increase with L at low temperatures, while they decrease with increasing L at high temperatures. These results strongly suggest the occurrence of the SG phase at low temperatures. The SG phase transition temperature is estimated to be T SG ∼ 0.19J from the lattice size dependences of these excess free-energies.KEYWORDS: Heisenberg spin-glass, stiffness, excess energy, excess free-energy, rotation, reversal §1. Introduction Spin-glasses have attracted great challenge for computational physics. It has been believed that the spin-glass (SG) phase transition occurs in three dimensions (3d) for the Ising model 1, 2, 3) but not for the XY and Heisenberg models. 4, 5, 6, 7) However, numerical studies during the last decade have revealed that the SG phase might be more stable than what were previously believed. For example, in the isotropic Ruderman-Kittel-Kasuya-Yoshida (RKKY) model, it was suggested that the SG phase transition takes place at a finite temperature. 8, 9) It was also suggested that, for the Ising model, the SG phase might be realized at low temperatures even in two dimensions (2d). 10,11,12,13) For the XY and Heisenberg SG models, Kawamura and coworkers took notice of the chirality described by three neighboring spins, and suggested that, in 3d, a chiral glass phase transition occurs at a finite temperature without the conventional SG order. 14,15,16,17,18) The basis of their suggestion is the stiffness of the system at zero temperature. 14, 15) They estimated θ c > 0 and θ s < 0 from the lattice size dependences of the chiral and the spin domain-wall energies, where θ c and θ s are the stiffness exponent of the chiralities and that of the spins, respectively.

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Section: §2 Model and Methodscontrasting

confidence: 53%

Stiffness of the Heisenberg Spin-Glass Model at Zero- and Finite-Temperatures in Three Dimensions

2001

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“…Additional evidences came from Monte Carlo simulations at finite temperature, 202,203,73 in which the Binder parameters for the magnetization and the chirality of the three-dimensional ±J Heisenberg model were computed. A common crossing of the curves for different system sizes was found in both Binder parameters.…”

Section: Continuous Spin Models In Three Dimensionsmentioning

confidence: 99%

Recent Progress in Spin Glasses

Kawashima

Rieger

2013

Frustrated Spin Systems

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We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials is also mentioned.The motivation that pulls researchers toward spin glasses is possibly not the potential future use of spin glass materials in "practical" applications. It is rather the expectation that there must be something very fundamental in systems with randomness and frustration. It seems that this expectation has been acquiring a firmer ground as the difficulty of the problem is appreciated more clearly. For example, a close relationship has been established between spin glass problems and a class of optimization problems known to be N P -hard. It is now widely accepted that a good (i.e. polynomial) computational algorithm for solving any one of N P -hard problems most probably does not exist. Therefore, it is quite natural to expect that the Ising spin glass problem, as one of the problem in the class, would be very hard to solve, which indeed turns out to be the case in a vast number of numerical studies. None the less, it is often the case that only numerical studies can decide whether a certain hypothetical picture applies to a given instance. Consequently, the major part of what we present below is inevitably a de-

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“…Lee and Young 27 gave for the Gaussian model T sg = 0.34(2) and ν = 1.2(2). Our estimate for ν is ν = 0.85 (15), where we use a value of z which will be obtained in Sec. III D (Eq.…”

Section: B Finite-time-scaling Analysesmentioning

confidence: 99%

“…The third theory argues a possibility of this simultaneous transition. Matsubara et al 15,16,17 showed several lines of evidence that the spin-glass transition occurs at a finite temperature. Nakamura et al 18,19 investigated the model by a nonequilibrium relaxation method 20,21,22,23,24 and obtained the consistent results.…”

Section: Introductionmentioning

confidence: 99%

Nonvanishing spin-glass transition temperature of the±JXYmodel in three dimensions

2004

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A three-dimensional ±J XY spin-glass model is investigated by a nonequilibrium relaxation method. We have introduced a new criterion for the finite-time scaling analysis. A transition temperature is obtained by a crossing point of obtained data. The scaling analysis on the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility shows that both transitions occur simultaneously. The result is checked by relaxation functions of the Binder parameters and the glass correlation lengths of the spin and the chirality. Every result is consistent if we consider that the transition is driven by the spin degrees of freedom.

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Stiffness of the Ground-State of a Heisenberg Spin-Glass Model

Cited by 33 publications

References 25 publications

Stiffness of the Heisenberg Spin-Glass Model at Zero- and Finite-Temperatures in Three Dimensions

Stiffness of the Heisenberg Spin-Glass Model at Zero- and Finite-Temperatures in Three Dimensions

Recent Progress in Spin Glasses

Nonvanishing spin-glass transition temperature of the±JXYmodel in three dimensions

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