Scaling functions for classical to quantum crossover in the transverse Ising model via an effective Wilsonian renormalization group approach in 4-e dimensions

The classical to quantum crossover, which occurs in the d-dimensional transverse Ising model decreasing the temperature to zero in the influence domain of the quantum critical point , is described by employing an effective Wilsonian renormalization group approach in 4-e dimensions. The basic ingredient of the treatment is the static action arising from a preliminary one-loop averaging over non zero frequency modes which enter the original quantum action. The crossover scaling functions for susceptibility are obtained as explicit functions of the temperature and the applied magnetic field.