A. Glazman

collaborators

Showing math.PRShow all

3 papers · 1 filter

math.PR2023

Delocalisation and continuity in 2D: loop O(2), six-vertex, and random-cluster models

Alexander Glazman, Piet Lammers

We prove the existence of macroscopic loops in the loop O(2) model with $\frac{1}{2} \leq x^{2} \leq 1$ or, equivalently, delocalisation of the associated integer-valued Lipschitz function…

math.PR2023

Phase diagram of the Ashkin-Teller model

Yacine Aoun, Moritz Dober, Alexander Glazman

The Ashkin-Teller model is a pair of interacting Ising models and has two parameters: $J$ is a coupling constant in the Ising models and $U$ describes the strength of the interacti…

math.PR2018

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

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 $x < \frac{1}{3} + ε (n)$ , for some suitable c…

Delocalisation and continuity in 2D: loop O(2), six-vertex, and random-cluster models

Phase diagram of the Ashkin-Teller model

Exponential decay in the loop O(n) model: n>1, x<3​1​+ε(n)

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