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

We study the magnetization mL(h, b) for the Ising model on a large but finite lattice square under the minus boundary conditions. Using known large-devia-tion results evaluating the balance between the competing effects of the minus boundary conditions and the external magnetic field h, we describe the details of its dependence on h as exemplified by the finite-size rounding of the infinite-volume magnetization discontinuity and its shift with respect to the infinite-volume transition point. KEY WORDS: Ising model; finite size scaling; first-order phase transitions. 1