%0 Generic %1 lees2019monotonicity %A Lees, Benjamin %A Taggi, Lorenzo %D 2019 %K XY model %R 10.1007/s00220-019-03647-6 %T Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N %U http://arxiv.org/abs/1902.07252 %X 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 $Z^d$, $d 3$, when $N N_>0$ and the inverse temperature $\beta$ is large enough. This is a new result when $N>2$ and extends the classical result of Fröhlich, Simon and Spencer (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 $N ın N_>0$, 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.

@misc{lees2019monotonicity, 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 $\mathbb{Z}^d$, $d \geq 3$, when $N \in \mathbb{N}_{>0}$ and the inverse temperature $\beta$ is large enough. This is a new result when $N>2$ and extends the classical result of Fr\"ohlich, Simon and Spencer (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 $N \in \mathbb{N}_{>0}$, 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.}, added-at = {2021-12-05T01:20:28.000+0100}, author = {Lees, Benjamin and Taggi, Lorenzo}, biburl = {https://www.bibsonomy.org/bibtex/25ef8d38595912299be47463a7d88179a/gzhou}, description = {Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N}, doi = {10.1007/s00220-019-03647-6}, interhash = {9c8d5ce4bfd8338bb0c32f278dfbe078}, intrahash = {5ef8d38595912299be47463a7d88179a}, keywords = {XY model}, note = {cite arxiv:1902.07252Comment: 27 pages, 4 Figures}, timestamp = {2021-12-05T01:20:28.000+0100}, title = {Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N}, url = {http://arxiv.org/abs/1902.07252}, year = 2019 }