{"product_id":"9783639056587","title":"Witten Laplacian Methods for Critical Phenomena","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.","brand":"VDM Verlag Dr. Mueller E.K.","offers":[{"title":"Default Title","offer_id":47041042120944,"sku":"9783639056587","price":64.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9783639056587_p0.jpg?v=1763728397","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9783639056587","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}