Analysis of the effect of surfaces on the tricritical behavior of systems

Publisher Website
Google Scholar
Abstract
The order parameter φ(z) of the φ6-dominated tricritical free energy functional is calculated for film and half-space geometries. Extrapolation length (Λ) boundary conditions are used to simulate the effect of the surface. Closed-form expressions for φ(z) of a film are given in terms of Weierstrass elliptic functions, or, alternatively, Jacobi elliptic functions. For a half-space, φ(z) is expressed in terms of hyperbolic functions. In the absence of an external field, it is shown that the phase transitions which the system can undergo may be classified as ordinary (Λ>0), urrface (Λ<0), and special (Λ=∞), like the φ4 theory for second-order phase transitions. The critical exponents for the order parameter at the surface are determined for each type of phase transition. A discussion of the free energy for the surface phase is also presented.