Critical Behavior of the Anisotropicn-Vector Model

The critical behavior of a system of n-component classical "spins"with anisotropic pair interactions is discussed using renormalization-group techniques for dimension d=4-ε. To first order in ε the correlation and susceptibility exponents in the isotropic limit are 2ν=γ=1+[(n+2)/2(n+8)]ε, while the anisotropy or crossover exponent is φ=1+[n/2(n+8)]ε. When n→∞ these expansions agree with exact spherical-model results. For $n=3$ and $d=3$ series expansions indicate φ1.2 (compared with γ1.38).