Exponential decay in the loop $O(n)$ model: $n>1$, $x<\frac{1}{\sqrt{3}}+\epsilon (n)$

Alexander Glazman, Ioan Manolescu

We show that the loop $O(n)$ model on the hexagonal lattice exhibits exponential decay of loop sizes whenever $n>1$ and $x<\frac{1}{\sqrt{3}}+\epsilon (n)$, for some suitable c…