6 papers
Exponential decay of transverse correlations for O(N) spin systems and related models
Benjamin Lees, Lorenzo Taggi
We prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary (non-zero) values of the external magnetic field and arbitrary spin dimension N > 1. Our…
Uniformly positive correlations in the dimer model and phase transition in lattice permutations on , , via reflection positivity
Lorenzo Taggi
Our first main result is that correlations between monomers in the dimer model in do not decay to zero when . This is the first rigorous result about correlat…
Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N
Benjamin Lees, Lorenzo Taggi
We provide a uniformly-positive point-wise lower bound for the two-point function of the classical spin model on the torus of , , when $N \in \mathbb…
Abelian oil and water dynamics does not have an absorbing-state phase transition
Elisabetta Candellero, Alexandre Stauffer, Lorenzo Taggi
The oil and water model is an interacting particle system with two types of particles and a dynamics that conserves the number of particles, which belongs to the so-called class of…
Shifted critical threshold in the loop model at arbitrary small
Lorenzo Taggi
In the loop model a collection of mutually-disjoint self-avoiding loops is drawn at random on a finite domain of a lattice with probability proportional to $${λ^{\# \mbox{ed…
Interacting self-avoiding polygons
Volker Betz, Helge Schäfer, Lorenzo Taggi
We consider a system of self-avoiding polygons interacting through a potential that penalizes or rewards the number of mutual touchings and we provide an exact computation of the c…