Quantum effects in a d-dimensional exactly solvable model for a structural phase transition

An exactly solvable d-dimensional model of a structural phase transition with a long-range anharmonic interaction is considered in the low temperature region Tc→0 when the quantum effects are essential. It is shown that the quantum fluctuations lead to a suppression of the phase transition. However, at Tc > 0 they do not change the critical behaviour. The latter becomes pure quantum mechanical at Tc=0 when the dimensional crossover is fulfilled, according to which the critical behaviour of a d-dimensional quantum system (Tc=0) and of a (d+1)-dimensional classical system (Tc<) becomes equivalent.