Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N

Benjamin T Lees, Lorenzo Taggi

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)

Abstract

We provide a uniformly-positive point-wise lower bound for the two-point 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 site-monotonicity property of the two-point 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 double-dimer model, and the loop representation of the classical spin O(N) model.
Original languageEnglish
Pages (from-to)487–520
Number of pages34
JournalCommunications in Mathematical Physics
Volume376
Early online date7 Dec 2019
DOIs
Publication statusE-pub ahead of print - 7 Dec 2019

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