New universality class in three dimensions?: the antiferromagnetic RP2 model

Ballesteros, H. G.; Fernández, L.A.; Martı́n-Mayor, V.; Sudupe, A. Muñoz

doi:10.1016/0370-2693(96)00358-9

Cited by 84 publications

(119 citation statements)

References 19 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: 63%

“…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.…”

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confidence: 92%

“…In summary, we have shown that the Heisenberg spin glass undergoes a spin glass transition in D = 3, by means of Monte Carlo simulation and FSS analysis [2,4,5]. We have adapted a lattice gauge theory algorithm [21], that thermalizes L = 32 systems, well beyond any previous spin glass simulation in D = 3.…”

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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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confidence: 92%

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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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“…[1] (Table II from now on), is surprisingly not even mentioned by Kawamura and Campbell. We used the quotients method [3], a numerically convenient form of Nightingale's phenomenological renormalization [4], that has been extremely useful in the study of disordered systems [5].…”

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Campos¹,

Cotallo-Abán

Martı́n-Mayor

et al. 2007

Phys. Rev. Lett.

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“…We refer the interested reader to a sample of the extensive literature on this subject [BFMS,BFMS2,BFMS3,KS,R]. Unfortunately, except for the rather trivial case of N = 2, these systems cannot be treated by the present methods.…”

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Intermediate phases in mixed nematic/Heisenberg spin models

Campbell

Chayes

1999

J. Phys. A: Math. Gen.

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Abstract. We prove that in three or higher dimensions, an isotropic, ferromagnetic, nearestneighbour perturbation of an O(N ) nematic liquid crystal model has an intermediate phase. In this intermediate phase, the liquid crystal order parameter is non-zero but the spontaneous magnetization is zero while at low temperatures, these systems exhibit magnetization. This paper concerns the (lattice) nematic liquid crystal model. Here, at each site i of a regular lattice, resides an N -dimensional spin variable, s i . (We will take | s i | = 1; for physical considerations, one focuses on N = 2 or 3.) This variable, in some approximation, is supposed to represent a rod-like molecule (or density thereof) that is symmetric about its centre. Thus the spin-spin interaction usually boils down to the square of the standard Heisenberg exchange interaction. If the coefficient is negative, the model is attractive; this is the case we consider. Such models can have a low-temperature phase, called the nematic phase. The nematic states are translation invariant and are characterized by the non-vanishing of the nematic order parameter, i.e. the matrixdoes not average to zero. Needless to say in these models the spins themselves have zero average at all temperatures. Standard mean-field theory (see, e.g., [dGP]) indicates a first-order transition for N 3 (but not for N = 2). Presumably this is the case in dimension three and higher as indicated by simulations and Bethe lattice calculations [BZCP, KJ] (see also [dGP, CL] and references therein). Such models have also been investigated mathematically in [AZ, Z] (and more recently [TI]; cf the remark below). For the standard nearest-neighbour model in d 3, the existence of a nematic phase was established in the first reference. In [Z] the low-dimensional long-range versions of these systems were studied with similar success. (However, to the authors' knowledge there is, as of yet, no rigorous statement concerning the order of the transitions.)Entirely different physics is exhibited in the 'antiferromagnetic' versions-where the coupling favours anti-alignment. We refer the interested reader to a sample of the extensive literature on this subject [BFMS, BFMS2, BFMS3, KS, R]. Unfortunately, except for the rather trivial case of N = 2, these systems cannot be treated by the present methods. (The technical obstructions will be clarified below.)In this paper, we wish to consider a situation where the liquid crystal molecules have some asymmetry along the axis of the rod, which will become physically relevant at sufficiently low 0305-4470/99/508881+07$30.00

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New universality class in three dimensions?: the antiferromagnetic RP2 model

Cited by 84 publications

References 19 publications

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

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

Camposet al.Reply:

Intermediate phases in mixed nematic/Heisenberg spin models

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