A measure is reflection positive for a reflection when for every observable supported in one reflected half. Product measures and suitable ferromagnetic interactions satisfy this property.
Gaussian domination bounds the partition function of a reflection-positive spin model under a mean-zero external source by the partition function times a Gaussian exponential involving the inverse lattice Laplacian.
The infrared bound controls the nonzero Fourier modes of a spin correlation by the inverse lattice dispersion. Its momentum integral is finite in dimension at least three and can force spontaneous magnetization at low temperature.
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