Real-space renormalization for structural phase transitions in the Ising universality class

A real-space renormalization scheme for calculating the thermodynamic properties of models with continuous variables on a lattice having phase transitions in the Ising universality class is described. The first renormalization transformation maps the initial model onto a spin-½ Ising model with generalized interactions, which is then analyzed by an Ising renormalization transformation or by other means. Two versions of this procedure are used to calculate the phase diagram of a double-well model for structural phase transitions, which is identical with the ${\phi }^4$ field theory on a lattice, in two dimensions. The results are in excellent agreement with the molecular-dynamics studies of Schneider and Stoll.