Revisiting the field-driven edge transition of the tricritical two-dimensional Blume-Capel model

We reconsider the tricritical Blume-Capel model on the square lattice with a magnetic field acting on the open boundaries in one direction. Periodic boundary conditions are applied in the other direction. We apply three types of Monte Carlo algorithms, local Metropolis updates, and cluster algorithms of the Wolff and geometric type, adapted to the symmetry properties of the model. Statistical analyses of the bulk magnetization, the bulk Binder ratio, the edge magnetization, and the connected product of the edge and bulk magnetizations lead to new results confirming the presence of a singular edge transition at H-sc approximate to 0.68, as we reported earlier [Phys. Rev. E 71, 026109 (2005)]. We provide a plausible answer concerning a discrepancy between the behavior of the edge Binder ratio reported in that work and our new results.