XXX Spin Chain: from Bethe Solution to Open Problems

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We present some open problems in the field of exactly solvable models. Two of the problems are related to the correlation functions of the XXX spin chain and the XXZ spin chain, one to the entropy of subsystems and one to the six vertex model with domain wall boundary conditions.
11 pages. Talk presented at the Solvay workshop BETHE ANSATZ: 75 YEARS LATER, October 19-21, 2006, Brussels, Belgium

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