The random-walk representation of classical spin systems and correlation inequalities |
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Authors: | David C. Brydges Jürg Fröhlich Alan D. Sokal |
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Affiliation: | 1. Department of Mathématics, University of Virginia, 22903, Charlottesville, VA, USA 2. Theoretische Physik, ETH-H?nggerberg, CH-8093, Zürich, Switzerland 3. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012, New York, NY, USA
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Abstract: | We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic ?4 lattice models. These inequalities state that the finite partial sums of the propagator-resummed perturbation expansion for the 4-point function form an alternating set of rigorous upper and lower bounds for the exact 4-point function. Generalizations to 2n-point functions are also given. A simple construction of the continuum ? d 4 quantum field theory (d<4), based on these inequalities, is described in a companion paper. |
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