A Monte Carlo Study of One-Dimensional Interfaces.

Abstract

We study numerically one-dimensional interfaces by a Monte Carlo technique, where an interface is viewed as a loop embedded in one-, two- and three-dimensional Euclidean spaces. Since an actual interface has a surface tension, the action of the interface is defined on the basis of certain characteristic features possessed by a surface tension. The action contains an area energy term and a bending energy term with a dimensionless constant called rigidity. We find that the interfaces become smooth (crumpled) when the rigidity becomes large (small), and that there are no phase transitions of the first or second order. We can think of the absence of the phase transitions as indicating that there is no rapid mixing of the two materials separated by one-dimensional interfaces when the temperature of the system changes slowly.