In a number of classical statistical-physical models, there exists acharacteristic dimensionality called the upper critical dimension above whichone observes the mean-field critical behavior. Instead of constructinghigh-dimensional lattices, however, one can also consider infinite-dimensionalstructures, and the question is whether this mean-field character extends toquantum-mechanical cases as well. We therefore investigate the transverse-fieldquantum Ising model on the globally coupled network and the Watts-Strogatzsmall-world network by means of quantum Monte Carlo simulations and thefinite-size scaling analysis. We confirm that both the structures exhibitcritical behavior consistent with the mean-field description. In particular, weshow that the existing cumulant method has a difficulty in estimating thecorrect dynamic critical exponent and suggest that an order parameter based onthe quantum-mechanical expectation value can be a practically useful numericalobservable to determine critical behavior when there is no well-defineddimensionality.
展开▼
