  We study two- and three-particle scattering in the O(3) non-linear sigma
model in 1+1 dimensions, focusing on the isospin-1 and isospin-2 channels for
two particles, and the isospin-3 channel for three. We perform numerical
simulations for four values of the physical volume, each at three lattice
spacings, using a three-cluster generalization of the cluster update algorithm,
and directly extrapolate the determined finite-volume energies to the continuum
at fixed physical volume. Lattice results for two particles are then compared
against exact predictions, obtained by combining analytic results for the
scattering phase shifts and the (1+1)-dimensional two-particle formalism that
relates these to finite-volume energies. Analogous comparisons in the
three-particle sector are underway, making use of the three-particle
relativistic-field-theory finite-volume formalism.
