Wulff construction : a global shape from local interaction
Author(s)
Bibliographic Information
Wulff construction : a global shape from local interaction
（Translations of mathematical monographs, v. 104）
American Mathematical Society, c1992
- Other Title
-
Kонструкция Вулфа : форма определяется локальным взаимодействием
Konstrukt︠s︡ii︠a︡ Vulfa : forma opredeli︠a︡etsi︠a︡ lokalʹnym vzaimodeǐstviem
Available at / 44 libraries
-
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:530.1/d6562070237930
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references (p. 201-204)
Description and Table of Contents
Description
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.
Table of Contents
Introduction Extremal properties of the Wulff functional Limit theorems Surface tension Large contours Proof of the main results.
by "Nielsen BookData"