Surface critical behavior of tricritical systems

We study the surface critical behavior of semi-infinite systems with an n-component order parameter and short-range interactions at a bulk tricritical point. The special surface transition is investigated in detail for space dimensionalities d=3-{ε}{≤}3 using field-theoretic renormalization-group methods. For {ε}>0 its infrared-stable fixed point is described by a Hamiltonian which contains a {}{φ}{→}⁴ surface interaction of strength O(ε1/2) in addition to the familiar {}{φ}{→}⁶ bulk interaction of strength O({ε}). For d{≡}3, logarithmic corrections of a non-power-law form appear. The renormalization of a proper continuum model is expounded and the implications of the results are discussed, especially with regard to the adsorption of polymers from a {θ} solution.