scholarly journals Sum Rule for the Eight-Vertex Model on Its Combinatorial Line

2013 ◽  
pp. 599-637 ◽  
Author(s):  
Paul Zinn-Justin
Keyword(s):  
Vertex Model ◽  
Sum Rule

scholarly journals Around the Razumov–Stroganov Conjecture: Proof of a Multi-Parameter Sum Rule

10.37236/1903 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
P. Di Francesco ◽  
P. Zinn-Justin
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Loop Model ◽  
Vertex Model ◽  
Sum Rule ◽  
Alternating Sign Matrices ◽  
Wall Boundary Conditions ◽  
Periodic Strip ◽  
Domain Wall Boundary Conditions

We prove that the sum of entries of the suitably normalized groundstate vector of the $O(1)$ loop model with periodic boundary conditions on a periodic strip of size $2n$ is equal to the total number of $n\times n$ alternating sign matrices. This is done by identifying the state sum of a multi-parameter inhomogeneous version of the $O(1)$ model with the partition function of the inhomogeneous six-vertex model on a $n\times n$ square grid with domain wall boundary conditions.

scholarly journals Cwebs beyond three loops in multiparton amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Building Blocks ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Abelian Gauge ◽  
Sum Rule ◽  
Combinatorial Properties ◽  
Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

Energy-weighted sum rule for Gamow-Teller giant resonances in high-spin isomeric states of N=Z nuclei

2021 ◽  
Vol 103 (1) ◽  
Author(s):  
M. Sasano ◽  
H. Sagawa ◽  
T. Suzuki ◽  
M. Honma
Keyword(s):  
High Spin ◽  
Weighted Sum ◽  
Giant Resonances ◽  
Sum Rule ◽  
Gamow Teller ◽  
Isomeric States

Raman sum rule and the relation to the infrared sum rule in La2-xSrxCuO4

2010 ◽  
Vol 470 ◽  
pp. S97-S98 ◽  
Author(s):  
S. Sugai ◽  
Y. Takayanagi ◽  
N. Hayamizu ◽  
T. Muroi ◽  
J. Nohara ◽  
...  
Keyword(s):  
Sum Rule

scholarly journals Scaling limit of the Z2 invariant inhomogeneous six-vertex model

2021 ◽  
Vol 965 ◽  
pp. 115337 ◽  
Author(s):  
Vladimir V. Bazhanov ◽  
Gleb A. Kotousov ◽  
Sergii M. Koval ◽  
Sergei L. Lukyanov
Keyword(s):  
Scaling Limit ◽  
Vertex Model

A new isotopic sum rule

1978 ◽  
Vol 73 (3) ◽  
pp. 503-504 ◽  
Author(s):  
P. Babu Rao ◽  
K.V. Siva Sarma ◽  
K. SreeRamamurty
Keyword(s):  
Sum Rule

scholarly journals Quantitative sum rule analysis of low-temperature spectral functions

2013 ◽  
Vol 87 (7) ◽  
Author(s):  
Nathan P. M. Holt ◽  
Paul M. Hohler ◽  
Ralf Rapp
Keyword(s):  
Low Temperature ◽  
Spectral Functions ◽  
Sum Rule ◽  
Rule Analysis

A new completely integrable bi-plane 2D vertex model

1993 ◽  
Vol 174 (5-6) ◽  
pp. 407-410 ◽  
Author(s):  
A.E. Borovick ◽  
S.I. Kulinich ◽  
V.Yu. Popkov ◽  
Yu.M. Strzhemechny
Keyword(s):  
Vertex Model ◽  
Completely Integrable
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