Quantum criticality of d-dimensional n-vector transverse Ising-like models

We have revisited quantum criticality of d- dimensional n-vector transverse Ising-like models by means of a one-loop renormalization group approach with temperature scaling. A careful analysis of the quantum regime for d ≤ 3 allows us to explore the low-temperature phase diagram and to derive new features which occur close to the quantum critical point within the disordered phase. In particular for d ≤ 3 a crossover of the shift exponent from the value ψ = d-1 ( as for d ≥ 3 ) to ψ = 2 is found decreasing the temperature to zero