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 Sjstrand. The book also
provides a complete discussion of the L2-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.
VDM Verlag Dr. Mueller E.K.
|Country of origin:
||229 x 152 x 6mm (L x W x T)
||Paperback - Trade
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