Study of the antiferromagnetic Blume-Capel model by using the partition function zeros in the complex temperature plane

Abstract

The critical temperature and the thermal scaling exponent of the square-lattice Blume-Capel model are obtained as functions of fugacity by calculating the partition function zeros in the complex temperature plane of the square-lattice Blume-Capel antiferromagnet for the first time. The thermal scaling exponent yt determines the specific-heat critical exponent and the correlation-length critical exponent. The value of yt = 2 indicates a strong first-order phase transition in two dimensions whereas yt = 1 corresponds to an Ising-class second-order phase transition. The full spectrum (from yt = 2 to yt = 1) of the thermal scaling exponent for the square-lattice Blume-Capel model is evaluated for the first time. The phase diagram of the square-lattice Blume-Capel model, including the tricritical point, is also obtained, and it is compared with other results in the literature.