The Landau-Ginzburg-Wilson model in 2 and 2+ϵ dimensions at low temperatures

By introducing a collective variable the two-dimensional Landau-Ginzburg-Wilson model (classical order parameter of non-rigid magnitude) may, if the order parameter dimension exceeds one, be solved at absolute zero. A low temperature expansion about this solution is developed. The low temperature expansion supports the hypothesis that d = 2 systems with a two-component order parameter will have a non-zero critical point, below which the susceptibility diverges, although no symmetry breaking occurs. The leading order temperature dependence of η is determined. In addition an ϵ expansion for systems of spatial dimension 2 + ϵ is developed. The critical exponents, calculated here to lowest order in ϵ, agree with those found for stiff spins.