Abstract
We provide a uniformlypositive pointwise lower bound for the twopoint function of the classical spin O(N) model on the torus of ℤ^푑, 푑≥3, when 푁∈ℕ>0 and the inverse temperature 훽 is large enough. This is a new result when 푁>2
and extends the classical result of Fröhlich et al. (Commun Math Phys 50:79–95, 1976). Our bound follows from a new sitemonotonicity property of the twopoint function which is of independent interest and holds not only for the spin O(N) model with arbitrary 푁∈ℕ>0, but for a wide class of systems of interacting random walks and loops, including the loop O(N) model, random lattice permutations, the dimer model, the doubledimer model, and the loop representation of the classical spin O(N) model.
Original language  English 

Pages (fromto)  487–520 
Number of pages  34 
Journal  Communications in Mathematical Physics 
Volume  376 
Early online date  7 Dec 2019 
DOIs  
Publication status  Epub ahead of print  7 Dec 2019 
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Profiles

Dr Benjamin T Lees
 Probability, Analysis and Dynamics
 School of Mathematics  Heilbronn Research Fellow
Person: Academic