Milchev A, Müller M, Binder K, Landau DP. Wedge filling and interface delocalization in finite Ising lattices with antisymmetric surface fields.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003;
68:031601. [PMID:
14524775 DOI:
10.1103/physreve.68.031601]
[Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2003] [Indexed: 05/24/2023]
Abstract
Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic LxLxL(y) Ising lattices with nearest neighbor ferromagnetic exchange and four free LxL(y) surfaces, at which antisymmetric surface fields +/-H(s) act, are studied for a wide range of linear dimensions (4</=L</=320, 30</=L(y)</=1000), in an attempt to clarify finite size effects on the wedge filling transition in this "double-wedge" geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature T(c) this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For L,L(y)--> infinity and T larger than the filling transition temperature T(f)(H(s)), this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For T<T(f)(H(s)), however, this interface is bound either to the wedge where the two surfaces with field -H(s) meet (then the total magnetization m of the system is positive) or to the opposite wedge (then m<0). The distance l(0) of the interface midpoint from the wedges is studied as T-->T(f)(H(s)) from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of l(0) for T>T(f)(H(s)) as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length xi(y) in the y direction along the wedges is also studied, and we find no transition for finite L and L(y)--> infinity. For L--> infinity the prediction l(0) proportional, variant (H(sc)-H(s))(-1/4) is verified, where H(sc)(T) is the inverse function of T(f)(H(s)) and xi(y) proportional, variant (H(sc)-H(s))(-3/4), respectively. We also find that m vanishes discontinuously at the filling transition. When the corresponding wetting transition is first order we also obtain a first-order filling transition.
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