The Role of Spin Anisotropy in the Unbinding of Interfaces

We study the ground state of a classical X-Y model with p ≥ 3-fold spin anisotropy D in a uniform external field, H. An interface is introduced into the system by a suitable choice of boundary conditions. For large D, as H → 0, we prove using an expansion in D−1 that the interface unbinds from the surface through an infinite series of layering transitions. Numerical work shows that the transitions end in a sequence of critical end points. PACS numbers: 0550; 6470; 7540D Typeset using REVTEX 1 When an interface unbinds from a surface it can do so through a first or second order transition or, on a lattice, via a sequence of first order layering transitions. In general the nature of the unbinding, or wetting, transition depends on the details of the microscopic interactions and external parameters such as the temperature and applied magnetic field [1,2]. In a discrete spin model at zero temperature long-range interactions are needed to stabilise series of first order layering transitions. However, if the interactions are short range, an infinite sequence of such transitions can occur at finite temperatures [3]. This results from competition between the localising effect of the binding potential and the entropic terms in the free energy which favour a delocalised interface. In this paper we aim to discuss the role of a hithertofore unexplored parameter on the unbinding transition: the spin anisotropy. We shall show that, as discrete spins soften, layering transitions can be stabilised in simple, short-range clock models, even at zero temperature. An expansion in inverse spin anisotropy allows us to prove that an infinite sequence of layering phase transitions exist. Moreover, because the interesting features occur at zero temperature it is possible to follow the phase diagram numerically for all values of the spin anisotropy. In particular we are able to demonstrate how the boundaries between the different interface phases end in critical end points and to pinpoint these with considerable precision. We consider the classical X-Y model in a magnetic field H with p-fold anisotropy D. The model is defined by the Hamiltonian