A position space renormalisation group approach to the compressible Ising model

Abstract

A position space renormalisation group procedure is developed for the compressible Ising model. The procedure is essentially a generalisation of the cell variable approach of Niemeijer and Van Leeuwen (1974) in that vibrational cell variables are introduced in addition to spin cell variables. The procedure is applied to the two-dimensional triangular lattice, the shearless square lattice. In both cases the rigid Ising fixed point is stable to spin-lattice coupling as long as the latter is small. Beyond a critical strength of the spin-lattice coupling, the system develops instability leading to, presumably, a first-order transition. For the shearless square lattice the conclusion is at variance with the exact result of Baker and Essam (1971), so the approximation is regarded as unreliable for larger values of the spin-lattice coupling (1971).