**Translations of Mathematical Monographs**

1992;
204 pp;
Hardcover

MSC: Primary 82;
Secondary 60; 85

**Print ISBN: 978-0-8218-4563-9
Product Code: MMONO/104**

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Individual Member Price: $75.20

# Wulff Construction: A Global Shape from Local Interaction

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*Roland Dobrushin; R. Kotecký; Senya Shlosman*

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

# Table of Contents

## Wulff Construction: A Global Shape from Local Interaction

#### Readership

Research mathematicians.