Transformation to soluble model for structural phase transition from (4 × 1) to (8 × “2”) of In-adsorbed Si(1 1 1) surface

The Ising model proposed previously for the structural phase transition from (4 × 1) to (8 × “2”) of In-adsorbed Si(1 1 1) surface, Hamiltonian of which is consisting of a two-spin interaction as well as a four-spin interaction is shown to be equivalent in thermodynamic properties to a soluble Ising model with two-spin interactions. Temperature dependence of the long range order and the transition temperature can now be determined from the exact formulae. Comparison between the simulation results and those from the exact formulae is made to see accuracy of the simulation.