SURFACE-TENSION, STEP FREE-ENERGY, AND FACETS IN THE EQUILIBRIUM CRYSTAL

Some aspects of the microscopic theory of interfaces in classical latt ice systems are developed. The problem of the appearance of facets in the (Wulff) equilibrium crystal shape is discussed, together with its relation to the discontinuities of the derivatives of the surface tens ion tau(n) (with respect to the components of the surface normal n) an d the role of the step free energy tau(step)(m) (associated with a ste p orthogonal to m on a rigid interface). Among the results are, in the case of the Ising model at low enough temperatures, the existence of tau(step)(m) in the thermodynamic limit, the expression of this quanti ty by means of a convergent cluster expansion, and the fact that 2 tau (step)(m) is equal to the value of the jump of the derivative partial derivative tau/partial derivative theta (when theta varies) at the poi nt theta = 0 [with n = (m(1) sin theta, m(2) sin theta, cos theta)]. F inally, using this fact, it is shown that the facet shape is determine d by the function tau(step)(m).