Critical behaviour of quantum compressible Ising models

Abstract

The Landau-Ginsburg free-energy functional (effective Hamiltonian) is derived for compressible Ising systems where the Ising spins are coupled with quantum phonon fields and a transverse field is present. In the zero transverse field case, the phonon dynamical modes also disappear from the effective Hamiltonian, which then compares with those studied by Sak and De Moura et al. in the non-quantum compressible Ising systems. In the presence of dynamics in the spin system (compressible transverse Ising system), the phonon modes get effectively coupled in the Hamiltonian and while at non-zero temperatures this does not affect the critical behaviour (which remains the same as in the non-quantum case), the presence of these dynamical modes effectively increases the lattice dimensionality by unity at zero-temperature transitions (T_c=0) where one observes the critical behaviour corresponding to a d+1 dimensional non-quantum compressible Ising model. The critical behaviour of a cooperative Jahn-Teller phase transition when T_c to 0 is also discussed.