Se p 19 96 Magnetization Profile in the d = 2 Semi - Infinite Ising Model and Crossover between Ordinary and Normal Transition

We theoretically investigate the spatial dependence of the order parameter of the two-dimensional semi-infinite Ising model with a free surface at or above the bulk critical temperature. Special attention is paid to the influence of a surface magnetic field h1 and the crossover between the fixed points at h1 = 0 and h1 = ∞. The sharp increase of the magnetization m(z) close to the boundary generated by a small h1, which was found by the present authors in the three-dimensional model, is also seen in two dimensions. There, however, the universal short-distance power law is modified by a logarithm, m(z) ∼ zκ ln z, where κ, the difference between the scaling dimensions of h1 and the bulk magnetization, has the exact value 3/8. By means of a phenomenological scaling analysis, the short-distance behavior can be related to the logarithmic dependence of the surface magnetization m1 on h1. Our results, which are corroborated by Monte Carlo simulations, provide a deeper understanding of the existing exact results concerning the local magnetization and relate the short-distance phenomena in two dimensions to those in higher dimensionality. PACS: 75.40.-s,75.40.Mg,68.35.Rh,05.50.+q Typeset using REVTEX ∗e-mail: [email protected] †e-mail: [email protected]