6533b7d5fe1ef96bd1263b86

RESEARCH PRODUCT

Ising systems with pairwise competing surface fields

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description

The magnetization distribution and phase behaviour of large but finite Ising simple cubic L × L × L lattices in d = 3 dimensions and square L × L lattices in d = 2 dimensions are studied for the case where four free boundaries are present, at which surface fields +Hs act on one pair of opposite boundaries while surface fields −Hs act on the other pair (in d = 3, periodic boundary conditions are used for the remaining pair). Both the distribution PL(m) of the global magnetization and also the distribution of the local magnetization m(x,z) are obtained by Monte Carlo simulations, where x and z denote the coordinates when the boundaries are oriented along the x-axis and z-axis (in d = 2); or along the xy-plane and zy-plane (in d = 3, where the periodic boundary condition applies in the y-direction). Varying the temperature T and linear dimension L it is found that a single bulk rounded phase transition occurs, which converges to the bulk transition temperature Tcb as , unlike other geometric arrangements of competing boundary fields, where a second transition occurs in the bulk due to interface formation or delocalization, related to wedge or corner filling or wetting transitions, respectively. In the present geometry, only precursors of wetting layers form on those boundaries where the field is oppositely oriented to the magnetization in the bulk and the thickness of these layers is found to scale like L1/2 (in d = 2) or lnL (in d = 3), respectively. These findings are explained in terms of a phenomenological theory based on the effective interface Hamiltonian and scaling considerations.