On the low-temperature critical behaviour of a quantum model of structural phase transitions

A quantum model describing structural phase transitions in an anharmonic crystal with long-range interaction (decreasing at large distances r as r(-d-sigma), where d is the space dimensionality and 0< sigma <= 2) is studied at low temperatures. A general expression for the specific heat capacity is derived in the low-temperature region of the T, lambda -phase diagram, where T is the temperature and lambda is a quantum parameter, associated with the external pressure or the amount of doping. It is shown that in the vicinity of the quantum critical point (T = 0, lambda = lambda(c)) this expression has a scaling form. The temperature dependence of the critical specific heat capacity c(T) is established in the three regions of the phase diagram (renormalized classical region, quantum critical region and quantum disordered region). From the results obtained one can see that c(T) similar to T-2d/sigma in the renormalized classical region and in the quantum critical region, and c(T) exponentially tends to zero in the quantum disordered region. The applicability of the results obtained to other models is discussed.