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Journal of Statistical Physics

, Volume 159, Issue 2, pp 380–392 | Cite as

Lattice Integrals of Motion of the Ising Model on the Strip

  • Alessandro Nigro
Article

Abstract

We consider the 2D critical Ising model on a strip with fixed boundary conditions. It is shown that for a suitable reparametrization of the known Boltzmann weights the transfer matrix becomes a polynomial in the variable \(\csc (4u)\), being \(u\) the spectral parameter. The coefficients of this polynomial are decomposed on the fixed boundaries Temperley–Lieb Algebra by introducing a lattice version of the local integrals of motion.

Keywords

Ising model Integrability Conformal field theory Temperley–Lieb algebra 

Notes

Acknowledgments

The author acknowledges financial support from Fondo Sociale Europeo (Regione Lombardia), through the grant Dote ricerca.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Dipartimento di Fisica and INFN- Sezione di MilanoUniversità degli Studi di Milano IMilanoItaly

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