Surface tension,step free energy,and facets in the equilibrium crystal

Some aspects of the microscopic theory of interfaces in classical lattice 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 tension (n) (with respect to the components of the surface normaln) and the role of the step free energy ^step(m) (associated with a step orthogonal tom on a rigid interface). Among the results are, in the case of the Ising model at low enough temperatures, the existence of ^step(m) in the thermodynamic limit, the expression of this quantity by means of a convergent cluster expansion, and the fact that 2^step(m) is equal to the value of the jump of the derivative / (when varies) at the point =0 withn=(m ₁ sin ,m ₂ sin , cos )]. Finally, using this fact, it is shown that the facet shape is determined by the function ^step(m).