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Register a new userWang-Landau study of the triangular Blume-Capel ferromagnet
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Authors
N.G. Fytas
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We report on numerical simulations of the two-dimensional Blume-Capel ferromagnet embedded in the triangular lattice. The model is studied in both its first- and second-order phase transition regime for several values of the crystal field via a sophisticated two-stage numerical strategy using the Wang-Landau algorithm. Using classical finite-size scaling techniques we estimate with high accuracy phase-transition temperatures, thermal, and magnetic critical exponents and we give an approximation of the phase diagram of the model.
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The effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel model are discussed. The system is studied in both the pure and disorder
Systems of particles in a confining potential exhibit a spatially dependent density which fundamentally alters the nature of phase transitions that occur. A specific instance of this situation, which is being extensively explored currently, concerns the properties of ultra-cold, optically trapped atoms. Of interest is how the superfluid-insulator transition is modified by the inhomogeneity, and, indeed, the extent to which a sharp transition survives at all. This paper explores a classical analog of these systems, the Blume-Capel model with a spatially varying single ion anisotropy and/or temperature gradient. We present results both for the nature of the critical properties and for the validity of the local density approximation which is often used to model the inhomogeneous case. We compare situations when the underlying uniform transition is first and second order.
We study the pure and random-bo
We investigate the scaling of the interfacial adsorption of the two-dimensional Blume-Capel model using Monte Carlo simulations. In particular, we study the finite-size scaling behavior of the interfacial adsorption of the pure model at both its first- and second-order transition regimes, as well as at the vicinity of the tricritical point. Our analysis benefits from the currently existing quite accurate estimates of the relevant (tri)critical-point locations. In all studied cases, the numerical results verify to a level of high accuracy the expected scenarios derived from analytic free-energy scaling arguments. We also investigate the size dependence of the interfacial adsorption under the presence of quenched bond randomness at the originally first-order transition regime (disorder-induced continuous transition) and the relevant self-averaging properties of the system. For this ex-first-order regime, where strong transient effects are shown to be present, our findings support the scenario of a non-divergent scaling, similar to that found in the original second-order transition regime of the pure model.
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: AF1 (two interpenetrating lattices with S = -1 and S = 1) and AF2 (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.
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