On the quantum critical behaviour of a model of structural phase transitions with long-range interaction

The pure quantum limit of an exactly solvable lattice model describing structural phase transitions in an anharmonic crystal with long-range interaction is considered. At the upper quantum critical dimension the free energy density at T = 0 in the neighbourhood of the quantum critical point is exactly calculated in terms of the Lambert W-function. For the three real physical dimensions, the exact results, obtained here, and the asymptotic ones are compared. It is pointed out that the Lambert W-function turns out to be a very effective tool for an exact computation of non-universal characteristics in the upper critical dimensions, especially in a broader neighbourhood of the critical region.