Combinatorial Bethe ansatz and ultradiscrete Riemann theta function with rational characteristics

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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9 pages

Scientific paper

10.1007/s11005-007-0162-2

The U_q(\hat{sl}_2) vertex model at q=0 with periodic boundary condition is
an integrable cellular automaton in one-dimension. By the combinatorial Bethe
ansatz, the initial value problem is solved for arbitrary states in terms of an
ultradiscrete analogue of the Riemann theta function with rational
characteristics.

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