A. Glazman

activity

20132023

most citedOn the transition between the disordered and antiferroelectric phases of the 6-vertex model

21 citations · 55 across the 10 of their papers we have counts for

collaborators

12 papers

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.PR2021★ 4 cited

Structure of Gibbs measures for planar FK-percolation and Potts models

Alexander Glazman, Ioan Manolescu

We prove that all Gibbs measures of the $q$ -state Potts model on $Z^{2}$ are linear combinations of the extremal measures obtained as thermodynamic limits under free or mono…

math.PR2020

Macroscopic loops in the loop O(n) model via the XOR trick

Nicholas Crawford, Alexander Glazman, Matan Harel +1

The loop $O (n)$ model is a family of probability measures on collections of non-intersecting loops on the hexagonal lattice, parameterized by a loop-weight $n$ and an edge-weight $…

math.PR2019★ 21 cited

On the transition between the disordered and antiferroelectric phases of the 6-vertex model

Alexander Glazman, Ron Peled

The symmetric six-vertex model with parameters $a, b, c > 0$ is expected to exhibit different behavior in the regimes $a + b < c$ (antiferroelectric), $∣ a - b ∣ < c \leq a + b$ (disordered) and $|…

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…

math.PR2018

Uniform Lipschitz functions on the triangular lattice have logarithmic variations

Alexander Glazman, Ioan Manolescu

Uniform integer-valued Lipschitz functions on a domain of size $N$ of the triangular lattice are shown to have variations of order $lo g N$ . The level lines of such function…

math.PR2017

Self-avoiding walk on $Z^{2}$ with Yang-Baxter weights: universality of critical fugacity and 2-point function

Alexander Glazman, Ioan Manolescu

We consider a self-avoiding walk model (SAW) on the faces of the square lattice $Z^{2}$ . This walk can traverse the same face twice, but crosses any edge at most once. The w…

math.PR2017

Macroscopic loops in the loop $O (n)$ model at Nienhuis' critical point

Hugo Duminil-Copin, Alexander Glazman, Ron Peled +1

The loop $O (n)$ model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n…

math-ph2016★ 17 cited

Discrete stress-energy tensor in the loop O(n) model

Dmitry Chelkak, Alexander Glazman, Stanislav Smirnov

We study the loop $O (n)$ model on the honeycomb lattice. By means of local non-planar deformations of the lattice, we construct a discrete stress-energy tensor. For $n \in [0, 2]$ , i…

math.PR2014

Connective constant for a weighted self-avoiding walk on $Z^{2}$

Alexander Glazman

We consider a self-avoiding walk on the dual $Z^{2}$ lattice. This walk can traverse the same square twice but cannot cross the same edge more than once. The weight of each…

math.PR2013★ 13 cited

On the probability that self-avoiding walk ends at a given point

Hugo Duminil-Copin, Alexander Glazman, Alan Hammond +1

We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Z^d for d>1. We show that the probability that a walk of length n ends at a point x te…

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

Phase diagram of the Ashkin-Teller model

Structure of Gibbs measures for planar FK-percolation and Potts models

Macroscopic loops in the loop O(n) model via the XOR trick

On the transition between the disordered and antiferroelectric phases of the 6-vertex model

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

Uniform Lipschitz functions on the triangular lattice have logarithmic variations

Self-avoiding walk on Z2 with Yang-Baxter weights: universality of critical fugacity and 2-point function

Macroscopic loops in the loop O(n) model at Nienhuis' critical point

Discrete stress-energy tensor in the loop O(n) model

Connective constant for a weighted self-avoiding walk on Z2

On the probability that self-avoiding walk ends at a given point

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

Self-avoiding walk on $Z^{2}$ with Yang-Baxter weights: universality of critical fugacity and 2-point function

Macroscopic loops in the loop $O (n)$ model at Nienhuis' critical point

Connective constant for a weighted self-avoiding walk on $Z^{2}$