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arXiv:hep-lat/9511003 · Physics Letters B

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

H.G. Ballesteros, L. A. Fernández, Víctor Martín-Mayor, A. Muñoz Sudupe

Published Jun 1, 1996• 80 citations
arXivHTMLPDF
DOI
10.1016/0370-2693(96)00358-9

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It is shown that a bosonic formulation of the double-exchange model, one of the classical models for magnetism, generates dynamically a gauge-invariant phase in a finite region of the phase diagram. We use analytical methods, Monte Carlo simulations and finite-size scaling analysis. We study the transition line between that region and the paramagnetic phase. The numerical results show that this transition line belongs to the universality class of the antiferromagnetic RP2 model. The fact that one can define a universality class for the antiferromagnetic RP2 model, different from the one of the O(N) models, is puzzling and somehow contradicts naive expectations about universality.
Quantum theory reads several of its quantities on the loops of configuration space rather than at its points: the inequivalent quantizations of a system are classified by the characters of the fundamental group (Schulman 1968; Laidlaw and DeWitt 1971), and the phase factors on loops give a complete description of a gauge field (Wu and Yang 1975). We propose a framework in which reading on loops is the rule. It has three elements: the site ℝℙ², realized in Euclidean space by the cross-cap; its covering S²↓ℝℙ², the only connected non-trivial covering of the site, hence its universal covering; and the reading, with values in a sheaf on the site. The obstruction of the site is the class a = w₁(ℝℙ²). Four known calculations are reread in this framework, and each reads the same class a: the Schrödinger equation on ℝℙ² and on SO(3) (sectors split by the parity of ℓ, or of 2j); the Dirac equation on ℝℙ² (a single type of Pin structure, in two copies, and an asymmetric spectrum); the two degrees of the reading (the holonomy −1 and the torsion class of H²(ℝℙ²; ℤ) are one element); and the 4π periodicity of spin ½ (the monodromy of SU(2)↓SO(3)). The thesis (Th) is that this framework offers a common perspective on scattered approaches. Numerical checks are supplied as scripts. This record contains the same paper in two versions: English (primary) and French (original). The French text prevails in case of discrepancy. — Ce dépôt contient le même texte en deux versions : anglaise (principale) et française (originale) ; le texte français fait foi.
We study spin glass behavior in a random Ising Coulomb antiferromagnet in two and three dimensions using Monte Carlo simulations. In two dimensions, we find a transition at zero temperature with critical exponents consistent with those of the Edwards-Anderson model, though with large uncertainties. In three dimensions, evidence for a finite-temperature transition, as occurs in the Edwards-Anderson model, is rather weak. This may indicate that the sizes are too small to probe the asymptotic critical behavior, or possibly that the universality class is different from that of the Edwards-Anderson model and has a lower critical dimension equal to three.