We investigate the use of global demons, a ''canonical dynamics'', as
an approach to simulating lattice regularized field theories. This det
erministically chaotic dynamics is non-local and non-hamiltonian, and
preserves the canonical measure rather than delta(H - E). We apply thi
s inexact dynamics to the 2D XY model, comparing to various implementa
tions of hybrid Monte Carlo, focusing on critical exponents and critic
al slowing down. In addition, we discuss a scheme for making energy no
n-conserving dynamical algorithms exact without the use of a Metropoli
s hit.