scholarly journals Six-vertex model on a finite lattice: Integral representations for nonlocal correlation functions

2021 ◽  
pp. 115535
Author(s):  
F. Colomo ◽  
G. Di Giulio ◽  
A.G. Pronko
Keyword(s):  
Correlation Functions ◽  
Finite Lattice ◽  
Integral Representations ◽  
Vertex Model ◽  
Nonlocal Correlation

scholarly journals THE 19-VERTEX MODEL AT CRITICAL REGIME |q|=1

2001 ◽  
Vol 16 (09) ◽  
pp. 1559-1578 ◽  
Author(s):  
TAKEO KOJIMA
Keyword(s):  
Quantum Group ◽  
Correlation Functions ◽  
Free Field ◽  
Integral Representations ◽  
Critical Regime ◽  
Vertex Operators ◽  
Vertex Model ◽  
Free Fermions

We study the 19-vertex model associated with the quantum group [Formula: see text] at critical regime |q|=1. We give the realizations of the vertex operators in terms of free bosons and free fermions. Using these free field realizations, we present integral representations for the correlation functions.

scholarly journals Free field construction for correlation functions of the eight-vertex model

1998 ◽  
Vol 516 (3) ◽  
pp. 623-651 ◽  
Author(s):  
Michael Lashkevich ◽  
Yaroslav Pugai
Keyword(s):  
Correlation Functions ◽  
Free Field ◽  
Vertex Model

scholarly journals Six-vertex Models and the GUE-corners Process

2018 ◽  
Vol 2020 (6) ◽  
pp. 1794-1881
Author(s):  
Evgeni Dimitrov
Keyword(s):  
Correlation Functions ◽  
Probability Distributions ◽  
Gibbs Measures ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Difference Operators ◽  
Vertex Model ◽  
Gaussian Unitary Ensemble ◽  
Vertex Models ◽  
Higher Spin

Abstract We consider a class of probability distributions on the six-vertex model, which originates from the higher spin vertex models of [13]. We define operators, inspired by the Macdonald difference operators, which extract various correlation functions, measuring the probability of observing different arrow configurations. For the class of models we consider, the correlation functions can be expressed in terms of multiple contour integrals, which are suitable for asymptotic analysis. For a particular choice of parameters we analyze the limit of the correlation functions through the steepest descent method. Combining this asymptotic statement with some new results about Gibbs measures on Gelfand–Tsetlin cones and patterns, we show that the asymptotic behavior of our six-vertex model near the boundary is described by the Gaussian Unitary Ensemble-corners process.

scholarly journals Correlation Functions of the Ising Model with Multisite Interaction on the Husimi Lattice

1998 ◽  
Vol 12 (23) ◽  
pp. 2349-2358 ◽  
Author(s):  
N. S. Ananikian ◽  
R. G. Ghulghazaryan ◽  
N. Sh. Izmailian
Keyword(s):  
Ising Model ◽  
Fixed Points ◽  
Coordination Number ◽  
Recurrence Relation ◽  
Correlation Functions ◽  
Nearest Neighbor ◽  
Bethe Lattice ◽  
Vertex Model ◽  
Analytical Expression ◽  
Husimi Lattice

We consider a general spin-1/2 Ising model with multisite interaction on the Husimi lattice with the coordination number q and derive an analytical expression of correlation functions for stable fixed points of the corresponding recurrence relation. We show that for q=2 our model transforms to the two-state vertex model on the Bethe lattice with q=3 and for the case q=3, with only nearest neighbor interactions, we transform our model to the corresponding model on the Bethe lattice with q=3, using the Yang–Baxter equations.

Boundary Correlation Functions of the gl (1|1) Supersymmetric Vertex Model

2008 ◽  
Vol 50 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Zhang Chen-Jun ◽  
Zhou Jian-Hua ◽  
Yue Rui-Hong
Keyword(s):  
Correlation Functions ◽  
Vertex Model
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