Spin Ising transcription of a lattice model of micellar solutions

Abstract

It is pointed out that the spin-1 Hamiltonian H=-J ${\mathcal{J}}_{〈\mathrm{ij}〉}$ $S_i$ $S_j$-K ${\mathcal{J}}_{〈\mathrm{ij}〉}$ $S_i^2$ $S_j^2$-C ${\mathcal{J}}_{〈\mathrm{ij}〉}$ ($S_i^2$ $S_j$+$S_i$ $S_J^2$)+Δ ${\mathcal{J}}_i$ $S_i^2$ with staggered field C represents the Widom-type lattice mixture of bifunctional molecules ab and AA with finite interactions. The structure of the mean-field phase behavior of the model micellar solution is provided partially by that of the symmetrical section of Griffiths’s three-component model.