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Fcc structure, while the sum runs over all pairs, (r,r'), of nearest- neighbor lattice si tes. L> JII ' planar ordering, "XY-like". Consequently the multicritical point occurs at zero anisotropy i. , when J 1.. l. y=- Jil R=O .... R=O ~""" I ..... .... - - - - .......... -- Heisenberg i~ ! Jn [see equation (27)]. The dotted curves represent the loci of zeros of QM(x,y) and RN(x,y) for a partial differential approximant, (i), using about half the currently available data. The intersection of the lines of zeros represent an estimate of the location of the multisingular point (xc,Yc): See Table I and note that Yc=l is the exact result.

Phys. A~, 1365. Rohrer, H. (1975) Phys. Rev. Lett. ~, 1638. E. (1972) see Gammel in Graves-Morris (1973b). W. J. (1973) J. Phys. A~, 1507. S. R. (1973) J. Phys. A~, 1498. F. and Glen, M. (1976) J. Phys. F. G. (1975) J. Phys. 37. A~, 1469. Symanzik, K. (1970) Commun. Math. Phys. 118, 227; - - (1971) Q, 49. J. (1972) Phys. Rev. B 2, 4529. G. E. (1972) Phys. Rev. Lett. 28, 240. G. and Kogut, J. (1974) Phys. Repts. 12C, 75. W. F. (1975) J. Phys. A~, 1761. E. (1975) Phys. Rev. B 11, 2689. Wynn, P. (1956) Math.

8) V(p) and V(p,~) are never positive, and they vanish at the densities of whatever bulk phases are stable at the given T and p. In Figures 6 and 7 we see plots of V(p) and of V(p,~) corresponding to those of w(p/T, -l/T;p) and w(p/T, -l/T;p,~) in Figures 3 and 4. jl'(T'Pl 11-K,~~~~1 I I I I I I ~--------------------------P-' ~ap P1iq Figure 5 STRUCTURE AND THERMODYNAMICS OF INTERFACES (a) 41 ( b) Figure 6 V( P, )=constont Figure 7 In a mixture of c independent chemical components we may distinguish the densities Pl,P2""'Pc of each.

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