| Witten Laplacian Methods For Critical Phenomena Contributor(s): Assane, Lo (Author) |
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ISBN: 3639056582 ISBN-13: 9783639056587 Publisher: VDM Verlag Dr. Mueller E.K. OUR PRICE: $50.27 Product Type: Paperback Published: September 2008 |
| Additional Information |
| BISAC Categories: - Mathematics |
| Physical Information: 0.22" H x 6" W x 9" (0.34 lbs) 108 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book provides a mathematically rigorous introduction of the Witten Laplacian methods in Statistical Mechanics. The method provides a new point of view, based on PDE techniques, to approach the problem of computing and estimating thermodynamic functions in classical continuous spin models. The method can be thought as a stronger and more flexible version of the Brascamp-Lieb inequalities and is based on an exact representation of the thermodynamic functions in terms of solutions to a second order partial differential equation, involving a deformation of the standard Laplace-Beltrami operator. The formula was initially introduced by Bernard Helffer and Johanne Sjöstrand. The book also provides a complete discussion of the L 2-Theory for the Witten Laplacian equations on zero and one forms. A detailed proof of the exponential decay of the n-point correlation functions is given, along with a new formula suitable for a direct proof of the analyticity of the pressure for certain unbounded models in Statistical Mechanics and Euclidean Field theory. |
