Computer simulation of the three-dimensional short-range Heisenberg spin glass

Olive, Jessica; Young, A. P.; Sherrington, David C.

doi:10.1103/physrevb.34.6341

Cited by 170 publications

(163 citation statements)

References 30 publications

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“…This is achieved by performing classical Monte Carlo simulations using a heat-bath algorithm. 30 In the context of our model, the heat-bath algorithm is efficient down to very low temperatures (T /J ′ ≈ 10 −6 ), and, therefore, it is possible to have insight into very low-energy phases. The details of this algorithm are discussed in Appendix A.…”

Section: A Ground State Manifoldmentioning

confidence: 99%

“…In order to study the dynamics of this Hamiltonian, we have performed Monte Carlo simulations using the heatbath algorithm to update the vector directions. 30 Each spin is assumed to be in contact with a heat bath and is immediately put into a local equilibrium with respect to the instantaneous effective field on it from the nearest neighbor spins:…”

Section: Appendix A: Monte Carlo Techniquementioning

confidence: 99%

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Freezing and large time scales induced by geometrical frustration

2003

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We investigate the properties of an effective Hamiltonian with competing interactions involving spin and chirality variables, relevant for the description of the trimerized version of the spin-1/2 kagome antiferromagnet. Using classical Monte Carlo simulations, we show that remarkable behaviors develop at very low temperatures. Through an order by disorder mechanism, the low-energy states are characterized by a dynamical freezing of the chiralities, which decouples the lattice into "dimers" and "triangles" of antiferromagnetically coupled spins. Under the presence of an external magnetic field, the particular topology of the chiralities induces a very slow spin dynamics, reminiscent of what happens in ordinary spin glasses.

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Section: A Ground State Manifoldmentioning

confidence: 99%

Section: Appendix A: Monte Carlo Techniquementioning

confidence: 99%

Freezing and large time scales induced by geometrical frustration

2003

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“…One example is a spin-glass transition problem in the ±J Heisenberg model in three dimensions. Olive et al 10 performed a finite-size-scaling analysis of the spin-glass susceptibility and concluded that the phase transition does not occur. Matsubara et al 16 reported in the preprint version that the same analysis may give a finite transition temperature.…”

Section: New Criterion For Scaling Analysismentioning

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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“…The sum in (2) runs over nearest neighbours of a cubic lattice with periodic boundary conditions. We use a heat-bath algorithm [18] in which the updated spin has the correct Boltzmann distribution for the instantaneous local field. This method has the advantage that a change in the spin orientation is always made.…”

Section: Simulation Detailsmentioning

confidence: 99%

Time and length scales in spin glasses

Young¹

2004

J. Phys.: Condens. Matter

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Abstract. We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. We briefly review the present theoretical understanding of the spectacular phenomena observed in experiments and describe new numerical results obtained in the first large-scale simulation of the nonequilibrium dynamics of the three dimensional Heisenberg spin glass. Why do we study spin glass dynamics?Spin glasses can be seen as one of the paradigms for the statistical mechanics of impure materials. Experimentally, however, the spin glass phase is always probed via nonequilibrium dynamic experiments, because the equilibration time of macroscopic samples is infinite. Simulations can probe equilibrium behaviour for very moderate sizes only, so that the thermodynamic nature of the spin glass phase is still a matter of debate. It is also as a model system that the glassy dynamics of spin glasses has been studied very extensively in experiments, simulations, and theoretically in the last two decades [1,2]. Although many theories account for the simplest experimental results, such as the aging phenomenon, early experiments revealed several other spectacular phenomena (rejuvenation, memory, etc.) that are harder to explain, allowing one to discriminate between various approaches [3].In recent years, several theoretical descriptions of the slow dynamics of spin glasses described the physics in terms of a distribution of length scales whose time, t, and temperature, T , evolution depends on the specific experimental protocol, as reviewed in Ref. [3]. Aging is described as the slow growth of a coherence length, ℓ T (t), reflecting quasi-equilibrium/nonequilibrium at shorter/larger length scales. Sensitivity to perturbations of quasi-equilibrated length scales accounts then for rejuvenation effects, while the strong temperature dependence of the growth law ℓ T (t) explains memory effects [4,5,6,7,8]. If early numerical studies revealed the existence of such a distribution of length scales [9], its physical relevance was critically discussed only relatively recently [10,11]. A major problem, however, is that most studies focused on the Edwards-Anderson model of an Ising spin glass, defined by the Hamiltonian

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Computer simulation of the three-dimensional short-range Heisenberg spin glass

Cited by 170 publications

References 30 publications

Freezing and large time scales induced by geometrical frustration

Freezing and large time scales induced by geometrical frustration

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

Time and length scales in spin glasses

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