  With the aim of studying the relevance and properties of critical slowing
down in Monte Carlo simulations of lattice quantum field theories we carried
out a high precision numerical study of the discretised two-dimensional
CP^{N-1} model at N=10 using an over-heat bath algorithm. We identify critical
slowing down in terms of slowly-evolving topological modes and present evidence
that other observables couple to these slow modes. This coupling is found to
reduce however as we increase the physical volume in which we simulate.
