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RESEARCH PRODUCT

Critical phenomena at surfaces

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Abstract The presence of free surfaces adds a rich and interesting complexity to critical phenomena associated with phase transitions occurring in bulk materials. We shall review Monte Carlo computer simulation studies of surface critical behavior in simple cubic Ising- and XY-models with nearest-neighbor interactions J in the bulk and Js at the surface. These studies allow the identification of various critical exponents and critical amplitude ratios involving both the critical behavior of local quantities and of surface excess corrections to the bulk. We consider both the “ordinary” transition (surface criticality controlled by the bulk) and the “special transition” (a multicritical point where the line of two-dimensional surface transitions merges with bulk criticality). Our results are used to test various predictions from scaling theories and from renormalization group expansions. If bulk and surface magnetic fields are included, wetting transitions are observed when the surface field competes with the order in the bulk. Our simulations confirm the suggestion that the surface scaling theory also controls the wetting phase diagrams near the bulk critical point. Finally pertinent experiments are briefly mentioned and directions of future research discussed.