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Further extensions of the high-temperature expansions for the two-dimensional classical XY model on the triangular and the square lattices

07/2008;
Source: arXiv

ABSTRACT The high-temperature expansions for the spin-spin correlation function of the two-dimensional classical XY (planar rotator) model are extended by two terms, from order 24 through order 26, in the case of the square lattice, and by five terms, from order 15 through order 20, in the case of the triangular lattice. The data are analyzed to improve the current estimates of the critical parameters of the models.

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    ABSTRACT: High-temperature bivariate expansions have been derived for the two-spin-correlation function in a variety of classical lattice XY (planar rotator) models in which spatially isotropic interactions among first-neighbor spins compete with spatially isotropic or anisotropic (in particular uniaxial) interactions among next-to-nearest-neighbor spins. The expansions, calculated for cubic lattices of dimensions d=1, 2, and 3, are expressed in terms of the two variables K1=J1/kT and K2=J2/kT, where J1 and J2 are the nearest-neighbor and the next-to-nearest-neighbor exchange couplings, respectively. This paper deals in particular with the properties of the d=3 uniaxial XY model (ANNNXY model) for which the bivariate expansions have been computed through the 18th order, thus extending by 12 orders the results so far available and making a study of this model possible over a wide range of values of the competition parameter R=J2/J1. Universality with respect to R on the critical line separating the paramagnetic and the ferromagnetic phases can be verified, and at the same time the very accurate determination γ=1.3177(5) and ν=0.6726(8) of the critical exponents of the susceptibility and of the correlation length, in the three-dimensional XY universality class, can be achieved. For the exponents at the multicritical (m,d,N)=(1,3,2) Lifshitz point the estimates γl=1.535(25), ν⊥=0.805(15), and ν∥=0.40(3) are obtained. Finally, the susceptibility exponent is estimated along the boundary between the disordered and the modulated phases.
    Physical review. B, Condensed matter 08/2008; 78(5). · 3.77 Impact Factor

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