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Register a new userWetting and interfacial adsorption in the Blume-Capel model on the square lattice
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We study the Blume-Capel model on the square lattice. To allow for wetting and interfacial adsorption, the spins on opposite boundaries are fixed in two different states, +1 and -1, with reduced couplings at one of the boundaries. Using mainly Monte Carlo techniques, of Metropolis and Wang-Landau type, phase diagrams showing bulk and wetting transitions are determined. The role of the non-boundary state, 0, adsorbed preferably at the interface between -1 and +1 rich regions, is elucidated.
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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 study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) $q$-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., $q = 3$, $4$, and $q = 8$, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point.
The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that, the second-order transition emerging under bond randomness from the first-order regime of the pure model, belongs to a new and distinctive universality class. The first finding reinforces the scenario of a single universality class for the 3d Ising model with the three well-known types of quenched uncorrelated disorder (bond randomness, site- and bond-dilution). The second, amounts to a strong violation of universality principle of critical phenomena. For this case of the ex-first-order 3d Blume-Capel model, we find sharp differences from the critical behaviors, emerging under randomness, in the cases of the ex-first-order transitions of the corresponding weak and strong first-order transitions in the 3d three-state and four-state Potts models.
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.
The critical properties of the spin-1 two-dimensional Blume-Capel model on directed and undi- rected random lattices with quenched connectivity disorder is studied through Monte Carlo simulations. The critical temperature, as well as the critical point exponents are obtained. For the undi- rected case this random system belongs to the same universality class as the regular two-dimensional model. However, for the directed random lattice one has a second-order phase transition for q < qc and a first-order phase transition for q > qc, where qc is the critical rewiring probability. The critical exponents for q < qc was calculated and they do not belong to the same universality class as the regular two-dimensional ferromagnetic model.
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