An exactly solvable modification of the planar Ising ferromagnet is proposed which has a roughening transition below the Curie temperature. The computation confirms the de Gennes-Fisher scaling theory of correlations with homogeneous surface fields, giving an exponent value A t = 2.PACS numbers: 05.50.+q, 75.10.HkThe nature of the interface, or domain wall, between oppositely magnetized phases of a ferromagnet below its Curie temperature T c has been the subject of considerable recent interest. 1 " 4 It has been realized that, even though there exists a well-defined specific incremental free energy for a domain wall, 5 ' 6 in many situations the actual structure of such a wall is averaged out by capillary fluctuations unless some external stabilizing force is applied.A phenomenology which is generally accepted is that the domain wall may undergo large fluctuations on a length scale determined by the area of the interface, but carries with it a local structure which, in the critical region, varies on the scale of the correlation length. It is to this local structure that the successful phenomenological theory developed by van der Waals, by Cahn and Hilliard, and by Fisk and Widom 7 refers.The following remarks relate to simple-cubic Ising ferromagnets in d dimensions. For d =2, the interface between phases with magnetization , ±m*, ra* being the spontaneous magnetization, is always diffuse for 0T>T R the interface is diffuse. A roughening transition is said to occur at T R . The evidence for this, which is not beyond dispute, deprives from series expansions 9 and Monte Carlo simulations. 10 A rigorous proof that there exists a T R

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An exact statistical mechanical derivation is given of the critical Casimir forces for Ising strips with arbitrary surface fields applied to edges. Our results show that the strength as well as the sign of the force can be controled by varying the temperature or the fields. An interpretation of the results is given in terms of a linked cluster expansion. This suggests a systematic approach for deriving the critical Casimir force which can be used in more general models.

A microscopic, driven lattice gas model is proposed for the dynamics and spatio-temporal fluctuations of the precursor film observed in spreading experiments. Matter is transported both by holes and particles, and the distribution of each can be described by driven diffusion with a moving boundary. This picture leads to a stochastic partial differential equation for the shape of the boundary, which agrees with the simulations of the lattice gas. Preliminary results for flow in a thermal gradient are discussed.PACS numbers: 68.08. Bc, 68.15+e, 64.60.Ht, 05.70.Np Spreading of involatile liquid drops on surfaces and fibers plays a significant role in many technologies, the efficient deployment of which requires detailed understanding of the underlying process [1,2]. Behavior at a macroscopic scale is accurately described by hydrodynamics [3], but experiments performed over the last 15 years or so have produced a surprise: in the case of complete wetting, the spreading drop, when examined on an atomic length scale in the direction normal to the substrate, is found to be preceded by a precursor film about one molecule thick; this can be followed laterally out to an extension of the order of 10 7 molecules diameter. At the horizontal resolving power of the technique used (ellipsometry), the precursor film is found to be flat and homogeneous. Its radius advances with time as √ t. Typical systems showing this class of behavior which can be investigated by ellipsometry are various silanes spreading over atomically flat Si(111) wafers with highly pure oxydised surfaces. With selected silanes, such systems even show dynamical layering with up to four superposed precursor films advancing as √ t, the layer directly in contact with the substrate being much faster than the others. As Ball observed over a decade ago [1], at that time there was hardly even a formative theory of such phenomena. Such theory must capture the experimentally determined diffusive behavior and, at the same time, explain how an extremely viscous, involatile material is transported from the reservoir to the precursor edge.A partial solution was first achieved by applying Molecular Dynamics to a droplet composed of spherical molecules with Lennard-Jones interactions [4]. The strength of these is adjusted to achieve sufficient involatility. Experimentally, the droplet is placed in contact with a substrate composed of much smaller units; this is therefore treated as a continuum for calculating the interaction of the spreading molecules with the substrate. Such a model shows a precursor film with the correct, diffusive behavior [4,5]. Monte Carlo (MC) lattice gas simulations in 3d [6,7] confirm this, and suggest a dual mechanism of matter transport involving on the one hand particles located in a supernatant layer directly placed above the precursor film, and on the other, holes in the precursor film itself. At the same time, essentially all the configurational change occurs at the boundary of the drop. However, so far these ideas just constitute a pictur...

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We propose a solid-on-solid-model description of the dynamics of wetting, using Langevin equations. The Gaussian version, appropriate to partial wetting, is solved exactly. The general version is solved using local equilibrium and scaling arguments. We obtain the dynamical contact angle, the shape of the profile near the substrate, and, for dry spreading, the occurrence, speed, and possible layering of a precursor film.

The eigenvalue problem for the transfer matrix of the two‐dimensional Ising lattice, with free boundaries perpendicular to the transfer direction, is solved. The mathematical mechanism which produces the asymptotic degeneracy of the eigenvalue spectrum below the bulk transition temperature is different from the case with cyclic boundary conditions. The results are used to calculate the two‐spin correlation function between two spins in the same edge of the lattice, and between two spins in opposite edges.