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Witten Laplacian Methods For Critical Phenomena
Angol
138 b
30 nap a termék visszaküldésére
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16 008
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10 692
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9 454
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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.
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