Quantum effects on criticality of an Ising model in scale-free networks: Beyond mean-field universality class

We study the effect of quantum fluctuations on the critical behavior of the Ising ferromagnetic phase transitions that do not belong to the mean-field universality class. A model system is considered, in which Ising spins are placed on the nodes of a scale-free network. Our Monte Carlo analysis shows that the critical exponents differ from those of mean-field phase transitions when degree exponent gamma is in the range 3 < gamma < 5. This confirms earlier analytic calculations based on ansatzes and approximation methods. As we apply quantum fluctuations by means of a magnetic field perpendicular to the Ising spin direction, the transition temperature T-c decreases with increasing magnetic field strength. We find, however, that the quantum fluctuations do not alter the critical exponents and the universality class remains unchanged.