Critical Phenomena under Non-Uniform External Force Fields

Abstract

Effects of non-uniform external force fields which vary in one direction, say, along the z-axis, on critical phenomena are studied in a general way. Nature of critical phenomena depends crucially on a type of the spectrum of a one-dimensional eigenvalue problem besides the symmetry breaking nature of the force. In particular, if the external potential maintains the symmetry of the order parameter and the lowest eigenvalue is isolated, there is a crossover from the d-dimensional bulk critical phenomena to the d-1-dimentional surface critical phenomena. On the other hand, if the external potential breaks the symmetry, a sharp phase transition disappears as for the liquid-gas transition under the gravitational field. The cases with periodic external potentials are also discussed.