The crossover between quantum and classical phase transitions in monolayers: a discrete φ4 model study

The crossover between quantum and classical phase transitions in monolayers is studied in the framework of the quantum discrete φ4 model by the quantum Monte Carlo simulations and analytical approximations. There are three parameters in the quantum discrete φ4 model: the reduced mass, the normalised temperature and the parameter determining the type of the transition. The crossovers between the quantum and the classical phase transitions and between the displacive and the order–disorder transition are controlled by these parameters. The critical values of the parameters of the quantum discrete φ4 model are extracted from the dependencies of the order parameter on the temperature at various values of other parameters of the model. The phase diagrams are obtained for a wide range of all parameters. The independent-mode and the mean-field approximation are used as analytical methods and show a qualitative agreement with numerical results.