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Journal of Physics Conference Series

Study of the Antiferromagnetic Blume-Capel Model on kagomé Lattice

Chi‐Ok Hwang, Sojeong Park, Wooseop Kwak

Published Sep 1, 2016• 2 citations
Publisher

Abstract

We study the anti-ferromagnetic (AF) Ising model and the AF Blume-Capel (BC) model on the kagomé lattice. Using the Wang-Landau sampling method, we estimate the joint density functions for both models on the lattice, and we obtain the exact critical magnetic fields at zero temperature by using the micro-canonical analysis. We also show the patterns of critical lines for the models from micro-canonical analysis.

DOI
10.1088/1742-6596/750/1/012016

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We study the anti-ferromagnetic (AF) Ising model and the AF Blume-Capel (BC) model on the kagomé lattice. Using the Wang-Landau sampling method, we estimate the joint density functions for both models on the lattice, and we obtain the exact critical magnetic fields at zero temperature by using the micro-canonical analysis. We also show the patterns of critical lines for the models from micro-canonical analysis.
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Abstract We investigate the density of states (DOS) in an antiferromagnetic spin‐system on a square lattice described by the Blume–Capel (BC) model. We use a new and very efficient simulation method, proposed by Wang and Landau, in which we estimate very precisely DOS by sampling in the space of energy. Then we calculate the thermodynamical averages like internal energy, free energy, specific heat and entropy. The BC model exhibits multicritical behaviour such as first‐ or second‐order transitions and tricritical points. It is known that the ground state of the model can exhibit two kinds of staggered antiferromagnetic phases: AF 1 (two interpenetrating lattices with S = –1 and S = 1) and AF 2 ( S = –1 and S = 0 for H < 0; S = 1 and S = 0 for H > 0). We analyze the coexistence of such phases at finite temperatures and determine border lines between them. To understand the microscopic nature of such boundaries we present also some results obtained with the standard Monte Carlo method. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We determinte the critical temperature of the spin-1 Blume-Capel (BC) model by using the derivative of the free energy with respect to the crystal field and call this quantity the “ preference ” parameter. We carry out simulations of the BC model on a two-dimensional square lattice by using the Wang-Landau sampling method. We measure the susceptibility and the critical temperature of the BC model by using the preference parameter and compare them with those obtained by using the magnetization. We find that the preference parameter works well for the BC model and improves the simulation performance.
The partition function zeros of the Ising model on a kagomé lattice in the complex magnetic-field plane are obtained. The properties of the Ising model on a kagomé lattice are not known in an external magnetic field. We estimate the joint density of states for the Ising model on a kagomé lattice in an external magnetic field by using the Wang-Landau sampling method. From the joint density of states, we evaluate its partition function zeros (so-called the Yang-Lee zeros) in the complex magnetic-field plane. For the first time, we investigate the unknown properties of the Ising model on a kagomé lattice in an external magnetic field by using its Yang-Lee zeros.
The susceptibility of the Ising model on a kagomé lattice has never been obtained. We investigate the properties of the kagomé-lattice Ising model by using the Wang-Landau sampling method. We estimate both the magnetic scaling exponent yh = 1.90(1) and the thermal scaling exponent yt = 1.04(2) only from the susceptibility. From the estimated values of yh and yt , we obtain all the critical exponents, the specific-heat critical exponent α = 0.08(4), the spontaneous-magnetization critical exponent β = 0.10(1), the susceptibility critical exponent γ = 1.73(5), the isothermalmagnetization critical exponent δ = 16(4), the correlation-length critical exponent ν = 0.96(2), and the correlation-function critical exponent η = 0.20(4), without using any other thermodynamic function, such as the specific heat, magnetization, correlation length, and correlation function. One should note that the evaluation of all the critical exponents only from information on the susceptibility is an innovative approach.