Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Yang-Baxter equation for PT invariant nineteen vertex models   We study the solutions of the Yang-Baxter equation associated to nineteen
vertex models invariant by the parity-time symmetry from the perspective of
algebraic geometry. We determine the form of the algebraic curves constraining
the respective Boltzmann weights and found that they possess a universal
structure. This allows us to classify the integrable manifolds in four
different families reproducing three known models besides uncovering a novel
nineteen vertex model in a unified way. The introduction of the spectral
parameter on the weights is made via the parameterization of the fundamental
algebraic curve which is a conic. The diagonalization of the transfer matrix of
the new vertex model and its thermodynamic limit properties are discussed. We
point out a connection between the form of the main curve and the nature of the
excitations of the corresponding spin-1 chains.

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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th