Parametric equation of state for then-vector model and polymers

Abstract

We introduce a new parametric form for the scaling equation of state of the n-vector model of magnetism correct to first order in ε=4-d. It is based on the equation of state of Schaaumlfer and Horner in a general parametric form proposed earlier by Schofield, Litster, and Ho. We integrate it to obtain the scaling part of the free energy F(T,H) of the n-vector model, correct to order ε, for general n. We use it to discuss the behavior of polymer solutions and equilibrium polymerization. This equation of state of the n<1 vector model shows no evidence of nonanalyticities in the H-T plane except at the critical point and on the coexistence curve, in disagreement with Gujrati’s claim for a singularity at H>0, T<$T_c$ which he interprets as signaling a ‘‘collapsed’’ phase for polymers in the limit n→0. We address several of the specific arguments of Gujrati which he uses to support his claim for this singularity. We also discuss the effect of the order of the limits n→0, H→0, and V→∞ on the nature of the polymerized state in equilibrium polymerization.