Critical behavior at dirty surfaces

The influence of quenched surface disorder — i.e. quenched disorder that is located at the bounding surface of a macroscopic system — on the surface critical behavior of such systems is investigated. To this end a class of semi-infinite continuum models of then-vector type with random surface interactions is studied. Both the case of surface transitions at a bulk critical point as well as that of surface transitions at a bulk tricritical point is considered. General irrelevance/relevance criteria of the Harris type are derived for both short-range and long-range correlated random surface interactions. These are used to assess the stability of the pure system critical behavior and to point out when random surface field or enhancement disorder is expected to be relevant.