Hardcover ISBN:  9780821845639 
Product Code:  MMONO/104 
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eBook ISBN:  9781470445157 
Product Code:  MMONO/104.E 
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AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845639 
eBook: ISBN:  9781470445157 
Product Code:  MMONO/104.B 
List Price:  $320.00 $242.50 
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AMS Member Price:  $256.00 $194.00 
Hardcover ISBN:  9780821845639 
Product Code:  MMONO/104 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445157 
Product Code:  MMONO/104.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845639 
eBook ISBN:  9781470445157 
Product Code:  MMONO/104.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 104; 1992; 204 ppMSC: Primary 82; Secondary 60; 85
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.
ReadershipResearch mathematicians.

Table of Contents

Chapters

Chapter I. Introduction

Chapter II. Extremal properties of the Wulff functional

Chapter III. Limit theorems

Chapter IV. Surface tension

Chapter V. Large contours

Chapter VI. Proof of the main results


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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.
Research mathematicians.

Chapters

Chapter I. Introduction

Chapter II. Extremal properties of the Wulff functional

Chapter III. Limit theorems

Chapter IV. Surface tension

Chapter V. Large contours

Chapter VI. Proof of the main results