Phase transitions in nanosystems caused by interface motion: the Ising bipyramid with competing surface fields

The phase behavior of a large but finite Ising ferromagnet in the presence of competing surface magnetic fields +/-H(s) is studied by Monte Carlo simulations and by phenomenological theory. Specifically, the geometry of a double pyramid of height 2L is considered, such that the surface field is positive on the four upper triangular surfaces of the bipyramid and negative on the lower ones. It is shown that the total spontaneous magnetization vanishes (for L --> infinity) at the temperature Tf(H), related to the "filling transition" of a semi-infinite pyramid, which can be well below the critical temperature of the bulk. The discontinuous vanishing of the magnetization is accompanied by a susceptibility that diverges with a Curie-Weiss power law, when the transition is approached from either side. A Landau theory with size-dependent critical amplitudes is proposed to explain these observations, and confirmed by finite size scaling analysis of the simulation results. The extension of these results to other nanosystems (gas-liquid systems, binary mixtures, etc.) is briefly discussed.