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Phys Rev E. 2019 Jan;99(1-1):012111. doi: 10.1103/PhysRevE.99.012111.

Monte Carlo study of the interfacial adsorption of the Blume-Capel model.

Author information

Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom.
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668, Warsaw, Poland.
Department of Physics, Section of Solid State Physics, University of Athens, Panepistimiopolis, GR 15784 Zografou, Greece.


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.


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