Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Lammers, Piet"'
Autor:
Glazman, Alexander, Lammers, Piet
We prove the existence of macroscopic loops in the loop O(2) model with $\frac12\leq x^2\leq 1$ or, equivalently, delocalisation of the associated integer-valued Lipschitz function on the triangular lattice. This settles one side of the conjecture of
Externí odkaz:
http://arxiv.org/abs/2306.01527
Autor:
Lammers, Piet
We consider the classical XY model (or classical rotor model) on the two-dimensional square lattice graph as well as its dual model, which is a model of height functions. The XY model has a phase transition called the Berezinskii-Kosterlitz-Thouless
Externí odkaz:
http://arxiv.org/abs/2301.06905
Autor:
Lammers, Piet
Height functions are random functions on a given graph, in our case integer-valued functions on the two-dimensional square lattice. We consider gradient potentials which (informally) lie between the discrete Gaussian and solid-on-solid model (inclusi
Externí odkaz:
http://arxiv.org/abs/2211.14365
Autor:
Lammers, Piet, Toninelli, Fabio
We study three Markov processes on infinite, unrooted, regular trees: the stochastic Ising model (also known as the Glauber heat bath dynamics of the Ising model), a majority voter dynamic, and a coalescing particle model. In each of the three cases
Externí odkaz:
http://arxiv.org/abs/2211.01033
Autor:
Lammers, Piet, Toninelli, Fabio
Publikováno v:
Combinatorics, Probability and Computing Volume 33 , Issue 1 , January 2024 , pp. 50 - 64
We study two models of discrete height functions, that is, models of random integer-valued functions on the vertices of a tree. First, we consider the random homomorphism model, in which neighbours must have a height difference of exactly one. The lo
Externí odkaz:
http://arxiv.org/abs/2208.12949
Autor:
Lammers, Piet, Ott, Sébastien
Publikováno v:
Probability Theory and Related Fields (2023)
The solid-on-solid model is a model of height functions, introduced to study the interface separating the $+$ and $-$ phase in the Ising model. The planar solid-on-solid model thus corresponds to the three-dimensional Ising model. Delocalisation of t
Externí odkaz:
http://arxiv.org/abs/2101.05139
Autor:
Lammers, Piet
Publikováno v:
Probability Theory and Related Fields (2021)
The interest is in models of integer-valued height functions on shift-invariant planar graphs whose maximum degree is three. We prove delocalisation for models induced by convex nearest-neighbour potentials, under the condition that each potential fu
Externí odkaz:
http://arxiv.org/abs/2012.09687
Autor:
Lammers, Piet, Tassy, Martin
Publikováno v:
Prob. Math. Phys. 5 (2024) 177-267
The motivation for this article is to derive strict convexity of the surface tension for Lipschitz random surfaces, that is, for models of random Lipschitz functions from $\mathbb Z^d$ to $\mathbb Z$ or $\mathbb R$. An essential innovation is that ra
Externí odkaz:
http://arxiv.org/abs/2004.15025
Autor:
Lammers, Piet, Tassy, Martin
Publikováno v:
Journal of Statistical Physics 179 (2020) 846-870
Using an alternative notion of entropy introduced by Datta, the max-entropy, we present a new simplified framework to study the minimizers of the specific free energy for random fields which are weakly dependent in the sense of Lewis, Pfister, and Su
Externí odkaz:
http://arxiv.org/abs/1907.05414
Autor:
Lammers, Piet
Publikováno v:
Annals of Probability 49 (2021) 1033-1066
Linde, Moore, and Nordahl introduced a generalisation of the honeycomb dimer model to higher dimensions. The purpose of this article is to describe a number of structural properties of this generalised model. First, it is shown that the samples of th
Externí odkaz:
http://arxiv.org/abs/1905.13216