Some Exact Results for the Electric Correlation Functions of the Eight-Vertex Model

1986 ◽  
Vol 56 (24) ◽  
pp. 2645-2648 ◽  
Author(s):  
Lee-Fen Ko ◽  
Barry M. McCoy
Keyword(s):  
Correlation Functions ◽  
Exact Results ◽  
Vertex Model

scholarly journals Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

2019 ◽  
Vol 34 (23) ◽  
pp. 1930011 ◽  
Author(s):  
Cyril Closset ◽  
Heeyeon Kim
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Partition Functions ◽  
Exact Results ◽  
Strongly Coupled ◽  
Seifert Manifolds ◽  
Recent Developments ◽  
Supersymmetric Gauge ◽  
Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

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

scholarly journals Forward-walking Green's Function Monte Carlo Method for Correlation Functions

1999 ◽  
Vol 52 (4) ◽  
pp. 637 ◽  
Author(s):  
M. Samaras ◽  
C. J. Hamer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
Exact Results ◽  
Expectation Values ◽  
Trial Wavefunction ◽  
Local Observables ◽  
Green's Function Monte Carlo

The forward-walking Green's Function Monte Carlo method is used to compute expectation values for the transverse Ising model in (1 + 1)D, and the results are compared with exact values. The magnetisation Mz and the correlation function p z (n) are computed. The algorithm reproduces the exact results, and convergence for the correlation functions seems almost as rapid as for local observables such as the magnetisation. The results are found to be sensitive to the trial wavefunction, however, especially at the critical point.

scholarly journals EQUATIONS FOR CORRELATION FUNCTIONS OF EIGHT-VERTEX MODEL: FERROMAGNETIC AND DISORDERED PHASES

1996 ◽  
Vol 10 (03n05) ◽  
pp. 101-116 ◽  
Author(s):  
M. YU. LASHKEVICH
Keyword(s):  
Correlation Functions ◽  
Analytical Approach ◽  
Vertex Model

The Kyoto group (Jimbo, Miwa, Nakayashiki et al.) has developed methods for calculating correlation functions of the eight-vertex model in antiferromagnetic phases. We extend these methods to ferromagnetic and disordered phases. We use Baxter’s symmetries to substantiate the validity of the analytical approach for these phases.

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