The four-dimensional<b><i>XY</i></b>spin glass

Jain, S.

doi:10.1088/0305-4470/29/15/004

Cited by 7 publications

(15 citation statements)

References 28 publications

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“…We are not aware of measurements of θ DW (0) or of T c for this system, although T c ≈ 0.95 has been reported for the four-dimensional XY SG with bimodal interactions. 26 Figure 4 shows a similar behavior for the d = 3 ISG. Again, x(T ) initially decreases as temperature increases.…”

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Size dependence of the internal energy in Ising and vector spin glasses

Katzgraber

Campbell

2003

Phys. Rev. B

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We study numerically the scaling correction to the internal energy per spin as a function of system size and temperature in a variety of Ising and vector spin glasses. From a standard scaling analysis we estimate the effective size correction exponent x at each temperature. For each system with a finite ordering temperature, as temperature is increased from zero, x initially decreases regularly until it goes through a minimum at a temperature close to the critical temperature, and then increases strongly. The behavior of the exponent x at and below the critical temperature is more complex than suggested by the model for the size correction that relates x to the domain-wall stiffness exponent.PACS numbers: 75.50. Lk, 05.50.+q, 75.40.Mg Since Gibbs, thermodynamic transitions have been classified according to the critical behavior of the specific heat, or equivalently of the critical temperature dependence of the internal energy. One of the disturbing features of the spin-glass transition has always been that there appears to be no thermodynamic signature whatsoever of the critical temperature, except in the mean-field limit. In finite dimensions, the specific-heat exponent α is strongly negative and the energy changes perfectly smoothly as a function of temperature through the critical temperature T c . 1 The standard scaling form for the finite-size correction to the internal energy per spin e(L) iswhere L represents the system size. An exponent θ E can be defined by θ E = d − x (d represents the space dimension). In Ising spin glasses (ISG) it has been surmised from "droplet" arguments 2,3,4 that this correction is directly related to the energy associated with domain walls, for which independent numerical measurements can also be carried out. Thus it is expected that at zero temperature θ E is identical to θ DW , the domain-wall stiffness exponent. This conjecture is related to the controversial question of the form of the elementary excitations in spin glasses, and the identity should be valid if periodic boundary conditions simply introduce supplementary domain walls. It is exact for Migdal-Kadanoff spin glasses. 4 While the argument was introduced for zero temperature, it has also been invoked for finite T . 3 At a continuous transition the singular part of the free energy divided by the temperature scales as length −d . Because (T − T c ) ∼ length −1/ν (see Refs. 5 and 6), if T c > 0,If T c = 0, θ DW = −1/ν at T = 0 and x(0) = d + 1/ν. 5 We have carried out Monte Carlo measurements of the size dependence of the energy as a function of temperature in the mean-field Sherrington-Kirkpatrick (SK) ISG model, in the Edwards-Anderson ISG with Gaussian interactions in dimensions 2, 3, and 4, in the gauge glass (GG) in dimensions 2, 3, and 4, and in the XY spin glass (XY SG) with Gaussian interactions in dimension 4. In all systems with a nonzero ordering temperature, x(T ) is strongly temperature dependent below as well as above T c . The effective exponent initially decreases progressively as T increases from...

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confidence: 55%

Size dependence of the internal energy in Ising and vector spin glasses

Katzgraber

Campbell

2003

Phys. Rev. B

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“…Here, we consider a vector spin-glass model, the fourdimensional XY spin glass, which is known to have a finite transition temperature 14 T c with T c ≃ 0.95. We perform Monte Carlo simulations for a modest range of sizes down to low temperatures (T ≃ 0.2T c ) using the parallel tempering Monte Carlo 15,16 technique.…”

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confidence: 99%

Monte Carlo simulations of the four-dimensionalXYspin glass at low temperatures

Katzgraber

Young

2002

Phys. Rev. B

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We report on the results for simulations of the four-dimensional XY spin glass using the parallel tempering Monte Carlo method at low temperatures for moderate sizes. Our results are qualitatively consistent with earlier work on the three-dimensional gauge glass as well as three-and four-dimensional Edwards-Anderson Ising spin glass. An extrapolation of our results would indicate that large-scale excitations cost only a finite amount of energy in the thermodynamic limit. The surface of these excitations may be fractal, although we cannot rule out a scenario compatible with replica symmetry breaking in which the surface of low-energy large-scale excitations is space filling.

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“…Using finite-size scaling and our earlier results for the spin glass transition [12], we shall find evidence for a simultaneous ordering of spin and chirality in four dimensions.…”

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confidence: 54%

“…Throughout, the temperature is given in units of the nearest-neighbour interaction. We recently reported the results concerning the spin glass transition for this model [12]. In this publication we concentrate on the chiral glass transition.…”

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confidence: 99%

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Chiral ordering in the four-dimensional planar spin glass

Jain

1997

Zeitschrift für Physik B Condensed Matter

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The chiral glass behaviour of the nearest-neighbour random-bond XY spin glass in four dimensions is studied by Monte Carlo simulations. A chiral glass transition at T cg = 0.90 ± 0.05 is found by a finite-size scaling analysis of the results. The associated chiral correlation-length exponent is estimated to be ν cg = 0.6 ± 0.1 and η cg ∼ 0.25. The values for the chiral critical temperature and the exponents are very similar to those reported recently for the spin glass transition in this model. The results strongly suggest a simultaneous ordering of spin and chirality in four dimensions.2

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The four-dimensionalXYspin glass

Cited by 7 publications

References 28 publications

Size dependence of the internal energy in Ising and vector spin glasses

Size dependence of the internal energy in Ising and vector spin glasses

Monte Carlo simulations of the four-dimensionalXYspin glass at low temperatures

Chiral ordering in the four-dimensional planar spin glass

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