Abstract
We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic ϕ4 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 ϕ 4 d quantum field theory (d<4), based on these inequalities, is described in a companion paper.
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Communicated by A. Jaffe
A. P. Sloan Foundation Research Fellow. Research supported in part by NSF grant MCS 79-02490
Research supported in part by NSF grant MCS 82-202599
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Brydges, D.C., Fröhlich, J. & Sokal, A.D. The random-walk representation of classical spin systems and correlation inequalities. Commun.Math. Phys. 91, 117–139 (1983). https://doi.org/10.1007/BF01206055
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DOI: https://doi.org/10.1007/BF01206055