2014 The n-component Landau-Ginzburg model with short range forces is examined for dimensionalities d less than two. For d, n such that Tc = 0, its solution reduces to the solution of the continuous Heisenberg-like model. The critical exponents and corresponding scaling laws are found for the Tc = 0 transitions and in particular ~ = 2 2014 d. LE JOURNAL DE PHYSIQUE LETTRES TOME 38, 15 JANVIER 1977, Classification Physics Abstracts 1.680 Much of the current work on phase transitions [1-3] is based upon the d-dimensional Ginzburg-Landau (G-L) functional H[ q>(x)] = acp2(x) + b~P4(x) + c[o~p(x)J2 . (1) Here ~p(x) is the n-component classical order parameter. Usually one assumes a = a’(T TMF) and a’, TMF, b and c, positive and finite. In fact, our derivation is valid under somewhat less restrictive requirements on a, b, c which will be stated in the course of the work. In general, the above functional has to be associated with a large momentum cut-off Q. This cut-off is required for ~ ~ 2, where it regularizes the ultraviolet singularities. The well known procedure which deals with the cut-off Q in the region 2 d 4 is the renormalization group [2, 4]. However, as has been already realized for d = 1 [1, 3, 5], for d 2 the ultraviolet singularities are absent, i.e. the cut-off can be omitted (Q = oo). The infrared singularities we have to deal with (for d 2) make Fe vanish at d 2, n = oo, without invalidating the G-L model itself [6]. The model also proved meaningful [1, 3, 5] for d = 1 and n arbitrary [1], and the present paper interpolates between the ~= 1, ~ > 1 [1, 5] and the n = oo, d 2 [6] results.