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We consider a general statistical mechanics model on a product of localspaces and prove that, if the corresponding measure is reflection positive,then several site-monotonicity properties for the two-point function hold. Asan application of such a general theorem, we derive site-monotonicityproperties for the spin-spin correlation of the quantum Heisenbergantiferromagnet and $XY$ model, we prove that such spin-spin correlations arepoint-wise uniformly positive on vertices with all odd coordinates -- improvingprevious positivity results which hold for the Ces\`aro sum -- and we derivesite-monotonicity properties for the probability that a loop connects twovertices in various random loop models, including the loop representation ofthe spin O(N) model, the double-dimer model, the loop O(N) model, latticepermutations, thus extending the previous results of \textit{Lees and Taggi(2019)}.

Site-monotonicity properties for reflection positive measures with applications to quantum spin systems