A theory of the equilibrium shape of crystal assuming minimal surface free energy was formulated at the beginning of the century by Wulff. This title presents a research monograph that considers the Wulff construction in the case of a two-dimensional Ising ferromagnet with periodic boundary conditions and at sufficiently low temperatures. Series: Translations of Mathematical Monographs. Num Pages: 204 pages. BIC Classification: PDE; PHFC. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 270. Weight in Grams: 601. . 1992. Hardcover. . . . .

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Bibliographic Details

Title: Wulff Construction: A Global Shape from Local Interaction (Translations of Mathematical Monographs)
Publisher: American Mathematical Society
Publication Date: 1992
Language: English
ISBN 10: 0821845632
ISBN 13: 9780821845639
Binding: Hardcover
Condition: New

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Synopsis

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 two-dimensional 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.

Language Notes

Text: English (translation)
Introduction: Russian

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