Multicritical behavior in the antiferromagnetic Blume–Capel model

Abstract

The existence of the fourth-order critical point has been found in the spin-1 Ising antiferromagnet with a single-ion potential and an external magnetic field involved by using the mean-field approximation calculation. The Monte Carlo simulation gives more accurate results and shows that no such phase transition occurs in the square lattice system. To show definitely that the fourth-order phase transition appears in three-dimensional systems, the simple cubic system is investigated by using Monte Carlo simulations. It was found that the decomposition of the tricritical point into a critical end point and a double critical end point appears in the phase diagram within a small range of the single-ion potential parameter. The location of the fourth-order critical point can also be estimated.