Finite-size scaling for the 2D Ising model with minus boundary conditions

We study the magnetization in(L)(h, beta) for the Ising model on a large bu t finite lattice square under the minus boundary conditions. Using known la rge-deviation results evaluating the balance between the competing effects of the minus boundary conditions and the external magnetic field h, we desc ribe the details of its dependence on h as exemplified by the finite-size r ounding of the infinite-volume magnetization discontinuity and its shift wi th respect to the infinite-volume transition point.