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 Zd, d≥ 3 , when N∈ N> 0 and the inverse temperature β is large enough. This is a new result when N> 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 N∈ 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.
Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N / Lees, B.; Taggi, L.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 376:1(2020), pp. 487-520. [10.1007/s00220-019-03647-6]
Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N
Taggi L.
2020
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 Zd, d≥ 3 , when N∈ N> 0 and the inverse temperature β is large enough. This is a new result when N> 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 N∈ 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.File | Dimensione | Formato | |
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