Lipatov Pomeron and the Heisenberg chain

Customary lattice methods are considered suitable for the description of the static, or low energy, nonperturbative properties of hadrons. Even though some progress has been made in studying the scattering length, form factors and the deep inelastic structure functions, the finite ultraviolet cut-off a ∼ 2GeV limits the application of classical lattice techniques mainly to the static phenomena. However, there exists an intriguing mapping, between the description of a high energy scattering and the one dimensional Heisenberg chain, which offers a possibility to use the methods of statistical physics to study the genuine high energy scattering. The typical high energy scattering is described by the Regge amplitude