Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 3-state Hamiltonians associated to solvable 33-vertex models   Using the nested coordinate Bethe ansatz, we study 33-vertex models, where
only one global charge with degenerate eigenvalues exists and each site
possesses three internal degrees of freedom. In the context of Markovian
processes, they correspond to diffusing particles with two possible internal
states which may be exchanged during the diffusion (transmutation). The first
step of the nested coordinate Bethe ansatz is performed providing the
eigenvalues in terms of rapidities. We give the constraints ensuring the
consistency of the computations. These rapidities also satisfy Bethe equations
involving $4\times 4$ R-matrices, solutions of the Yang--Baxter equation which
implies new constraints on the models. We solve them allowing us to list all
the solvable 33-vertex models.

34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
19
The categories of this paper are: eess
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The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio