Crossover Exponent φ for Spin Systems

Abstract

For the S = ∞ (classical) anisotropic Heisenberg model on sc, bcc, and fcc lattices, the high temperature series expansion coefficients of the susceptibility have been obtained as polynomials in the anisotropy parameter to orders 9(sc, bcc), and 8 (fcc). High temperature expansions of the derivatives of the susceptibility with respect to the anisotropic deviating field g have been used to determine, from scaling assumptions, the crossover exponent φ= 1.25± 0.015. This result has been confirmed by extending the same analysis to the specific heat and to the second moment of the correlation function. For the S =∞ (classical) XY model and for the planar (two component, classical) spin model on sc, bcc, and fcc lattices we find, by the same methods, φ = 1.175 ± 0.015 for both models.