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Lattice Integrals of Motion of the Ising Model on the Strip

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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.

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Acknowledgments

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

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Authors and Affiliations

  1. Dipartimento di Fisica and INFN- Sezione di Milano, Università degli Studi di Milano I, Via Celoria 16, 20133, Milano, Italy

    Alessandro Nigro

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  1. Alessandro Nigro
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Correspondence to Alessandro Nigro.

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Nigro, A. Lattice Integrals of Motion of the Ising Model on the Strip. J Stat Phys 159, 380–392 (2015). https://doi.org/10.1007/s10955-015-1186-0

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  • DOI: https://doi.org/10.1007/s10955-015-1186-0

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