Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03643-w
Abstract: In this paper we consider the stochastic six-vertex model on a cylinder with arbitrary initial data. First, we show that it exhibits a limit shape in the thermodynamic limit, whose density profile is given by… read more here.
Keywords: vertex model; limit; stochastic six; six vertex ... See more keywords
Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure
Sign Up to like & getrecommendations! Published in 2020 at "Probability Theory and Related Fields"
DOI: 10.1007/s00440-020-00966-x
Abstract: In this paper we consider the Higher Spin Six Vertex Model on the lattice $${\mathbb {Z}}_{\ge 2} \times {\mathbb {Z}}_{\ge 1}$$ . We first identify a family of translation invariant measures and subsequently we study… read more here.
Keywords: spin six; vertex model; model; higher spin ... See more keywords
Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
Sign Up to like & getrecommendations! Published in 2019 at "Nuclear Physics B"
DOI: 10.1016/j.nuclphysb.2018.12.011
Abstract: Abstract We consider several anisotropic extensions of the Belavin model, and show that integrability holds also for the massive case for some specific relations between the coupling constants. This is done by relating the S-matrix… read more here.
Keywords: anisotropic extensions; vertex model; integrability; solutions eight ... See more keywords
Three-partite vertex model and knot invariants
Sign Up to like & getrecommendations! Published in 2022 at "Physica A: Statistical Mechanics and its Applications"
DOI: 10.1016/j.physa.2022.127283
Abstract: This work dedicated to the consideration of the construction of a representation of braid group generators from vertex models with N -states, which provides a great way to study the knot invariant. An algebraic formula… read more here.
Keywords: knot invariant; three partite; partite vertex; vertex model ... See more keywords
On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Statistical Mechanics: Theory and Experiment"
DOI: 10.1088/1742-5468/ab7748
Abstract: The transfer matrix of the square-lattice eight-vertex model on a strip with L > 1 vertical lines and open boundary conditions is investigated. It is shown that for vertex weights a, b, c, d that… read more here.
Keywords: open boundary; eight vertex; transfer matrix; boundary conditions ... See more keywords
Sum rules for the supersymmetric eight-vertex model
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Statistical Mechanics: Theory and Experiment"
DOI: 10.1088/1742-5468/abda28
Abstract: The eight-vertex model on the square lattice with vertex weights a, b, c, d obeying the relation (a 2 + ab)(b 2 + ab) = (c 2 + ab)(d 2 + ab) is considered. Its… read more here.
Keywords: vertex model; sum rules; supersymmetric eight; eight vertex ... See more keywords
On the partition function of the Sp(2n) integrable vertex model
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Statistical Mechanics: Theory and Experiment"
DOI: 10.1088/1742-5468/acc730
Abstract: We study the partition function per site of the integrable Sp(2n) vertex model on the square lattice. We establish a set of transfer matrix fusion relations for this model. The solution of these functional relations… read more here.
Keywords: integrable vertex; partition; vertex model; partition function ... See more keywords
A Vertex Model for LLT Polynomials
Sign Up to like & getrecommendations! Published in 2021 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnab165
Abstract: We describe a novel Yang–Baxter integrable vertex model. From this vertex model we construct a certain class of partition functions that we show are essentially equal to the LLT polynomials of Lascoux, Leclerc, and Thibon.… read more here.
Keywords: model; llt polynomials; vertex model; model llt ... See more keywords
Geometrical characterization of active contraction pulses in epithelial cells using the two-dimensional vertex model
Sign Up to like & getrecommendations! Published in 2022 at "Journal of the Royal Society Interface"
DOI: 10.1098/rsif.2021.0851
Abstract: Several models have been proposed to describe the dynamics of epithelial tissues undergoing morphogenetic changes driven by apical constriction pulses, which differ in where the constriction is applied, either at the perimeter or in the… read more here.
Keywords: cell; two dimensional; vertex model; using two ... See more keywords
Hyperbolic fracton model, subsystem symmetry, and holography. II. The dual eight-vertex model
Sign Up to like & getrecommendations! Published in 2019 at "Physical Review B"
DOI: 10.1103/physrevb.100.245138
Abstract: The discovery of fracton states of matter opens up an exciting, largely unexplored field of many-body physics. Certain fracton states' similarity to gravity is an intriguing property. In an earlier work [Phys. Rev. B 99,… read more here.
Keywords: vertex model; eight vertex; fracton model; model ... See more keywords
Six-vertex model and Schramm-Loewner evolution.
Sign Up to like & getrecommendations! Published in 2017 at "Physical Review E"
DOI: 10.1103/physreve.95.052146
Abstract: Square ice is a statistical mechanics model for two-dimensional ice, widely believed to have a conformally invariant scaling limit. We associate a Peano (space-filling) curve to a square ice configuration, and more generally to a… read more here.
Keywords: schramm loewner; vertex model; ice; six vertex ... See more keywords