Two-Dimensional and Layered Structure in the Discrete φ~4 Model

摘要

The properties of phase transitions in two-dimensional and layered systems are investigated on the basis of a discrete φ~4 model by numerical and analytical methods. The only parameter a of the discrete φ~4 model determines the behavior of the system and makes it possible to investigate phase transitions ranging from transitions of the displacement type (a → +0) to order-disorder type (a → +∞). The behavior of a two-dimensional system is investigated in a wide range of values of the parameter a. The temperature dependences of the squared order parameter η~2(T) and the phase transition temperature T_c as a function of the thickness N of the system are obtained for three characteristic values of the parameter a using the Monte Carlo method. The properties of phase transitions in the discrete φ~4 model are investigated on the basis of the mean-field approximation and the independent-mode approximation. The results obtained in the numerical experiments are compared with the analytical approximations. It is shown that the mean-field approximation qualitatively describes the behavior of the phase-transition temperature T_c as a function of the thickness N of the system for a wide range of values of the parameter a, and the independent-mode approximation describes quantitatively, to within 5%, the results of the numerical simulation for small values of a.