Momentum-shell recursion relations, anisotropic spins, and liquid crystals in2+εdimensions

We describe in detail how to construct momentum-shell recursion relations for classical fixed-length spins in $d=2+\epsilon$ dimensions. The theory is then applied to anisotropic spin systems and to a model of nematic liquid crystals. We also develop a trajectory-integral formalism, which is used to produce the free energy, magnetization, and susceptibilities of isotropic spin systems to first order in $\epsilon =d-2\mathrm{}$.