Quantum criticality of d-dimensional n-vector transverse Ising-like models: New renormalization group features for d≤3

We revisit quantum criticality of d-dimensional n-vector transverse Ising-like models by means of a conventional one-loop renormalization group (RG) approach with temperature scaling. Focusing on dimensionalities d≤3, a careful analysis of the quantum regime allows us to explore the low-temperature phase diagram and to derive new features which occur close to but below 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 by decreasing the temperature to zero. Besides we provide information about the low-temperature physics within the thermally disordered region usually ignored in the literature. A similar scenario takes place for d=3, but now logarithmic corrections to the mean-field power-law behavior are involved.