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
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
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"