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We study two- and three-particle scattering in the O(3) non-linear sigmamodel in 1+1 dimensions, focusing on the isospin-1 and isospin-2 channels fortwo particles, and the isospin-3 channel for three. We perform numericalsimulations for four values of the physical volume, each at three latticespacings, using a three-cluster generalization of the cluster update algorithm,and directly extrapolate the determined finite-volume energies to the continuumat fixed physical volume. Lattice results for two particles are then comparedagainst exact predictions, obtained by combining analytic results for thescattering phase shifts and the (1+1)-dimensional two-particle formalism thatrelates these to finite-volume energies. Analogous comparisons in thethree-particle sector are underway, making use of the three-particlerelativistic-field-theory finite-volume formalism.

Two- and three-particle scattering in the (1+1)-dimensional O(3) non-linear sigma model