Analytic results for a phase transition in a planar array of chains

Phase transitions in low-dimensional ψ 4 systems

“…The authors suggest a general behaviour of the form t c c y ; withan index depending on the number of components of the order parameter and the dimensionality of the array. However, for a planar array of Ising chains, and of Ginzburg-Landau chains with real order parameter, they obtained, in the mean …eld approximation, a di¤erent behaviour of the critical temperature, t c 1= ln (c y =c) Let us investigate now the behaviour of the averaged …eld intensity for this system, < 2 2D > : The free energy of a planar array of chains was obtained recently using the Stoeckly-Scalapino approach [21]. The relevant part of the free energy, near the transition temperature, is given by…”