Crossover and scaling in one dimension

Abstract
The crossover and the scaling laws are derived for the n ≽ 1 Ginzburg-Landau model of weakly coupled linear chains. The results are obtained through the analogy with the weakly coupled anharmonic oscillators, the spectrum of which obeys a homogeneity relation of the Widom type. For n > 1, the crossover index ϕ and the transition temperature index ψ satisfy ϕ = ψ = 2