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Journal Articles Journal of Physics A: Mathematical and Theoretical Year : 2014

Arctic curves of the octahedron equation

Abstract

We study the octahedron relation (also known as the $A_{\infty}$ $T$-system), obeyed in particular by the partition function for dimer coverings of the Aztec Diamond graph. For a suitable class of doubly periodic initial conditions, we find exact solutions with a particularly simple factorized form. For these, we show that the density function that measures the average dimer occupation of a face of the Aztec graph, obeys a system of linear recursion relations with periodic coefficients. This allows us to explore the thermodynamic limit of the corresponding dimer models and to derive exact "arctic" curves separating the various phases of the system.

Dates and versions

cea-01002519 , version 1 (06-06-2014)

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P. Di Francesco, R. Soto-Garrido. Arctic curves of the octahedron equation. Journal of Physics A: Mathematical and Theoretical, 2014, 47 (28), pp.285204. ⟨10.1088/1751-8113/47/28/285204⟩. ⟨cea-01002519⟩
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