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The European Physical Journal B

Phase transition in the Blume-Capel model with second neighbour interaction

M. Badehdah, Smain Bekhechi, A. Benyoussef, M. Touzani

Published Sep 1, 1998• 18 citations
Publisher
DOI
10.1007/s100510050400

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Phase diagram and critical phenomena of a frustrated Blume–Capel model with alternating single-ion anisotropy ±D, nearest- and next-nearest-neighbour exchange interactions with equal magnitude J are studied by the Monte Carlo simulations using Wang–Landau sampling and nonequilibrium relaxation method. The collinear ordered phase due to next-nearest-neighbour interaction and partial ordered phase due to alternating anisotropy are confirmed together with a paramagnetic phase. We obtained the numerical results which strongly suggests that a single phase transition at D=0 splits into two Ising lines as soon as D is switched on. With the increase of D, the critical point of the easy-axis sublattice stays on a usual Ising-like critical line while that of the easy-plane sublattice passes through the tricritical point and the transition becomes of the first order as in the usual Blume–Capel model.
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 y t determines the specific-heat critical exponent and the correlation-length critical exponent. The value of y t = 2 indicates a strong first-order phase transition in two dimensions whereas y t = 1 corresponds to an Ising-class second-order phase transition. The full spectrum (from y t = 2 to y t = 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.