Translations of Mathematical Monographs 1992; 204 pp; hardcover Volume: 104 ISBN10: 0821845632 ISBN13: 9780821845639 List Price: US$94 Member Price: US$75.20 Order Code: MMONO/104
 A theory of the equilibrium shape of crystal assuming minimal surface free energy was formulated at the beginning of the century by Wulff. Assuming that the anisotropic interfacial free energy (depending on the orientation of the interface with respect to the crystal axes) is known, the Wulff construction yields the shape of crystal in equilibrium and allows one to understand its main features. This research monograph considers the Wulff construction in the case of a twodimensional Ising ferromagnet with periodic boundary conditions and at sufficiently low temperatures. Namely, the authors investigate the phenomenon of phase separation in a (small) canonical ensemble characterized by a fixed total spin in a finite volume. Its value is chosen to lie in the interval between the spontaneous magnetizations of pure phases. Heuristically, the main result can be stated this way: a droplet of one phase immersed in the opposite one will be formed with the separation line following with high accuracy the shape yielded by the Wulff construction. The book brings the reader through the entire development of the proof of this result. Readership Research mathematicians. Table of Contents  Introduction
 Extremal properties of the Wulff functional
 Limit theorems
 Surface tension
 Large contours
 Proof of the main results
