  We analyze the autocorrelations for the LHMC algorithm in the context of free
field theory. In this case this is just Adler's overrelaxation algorithm. We
consider the algorithm with even/odd, lexicographic, and random updates, and
show that its efficiency depends crucially on this ordering of sites when
optimized for a given class of operators. In particular, we show that, contrary
to previous expectations, it is possible to eliminate critical slowing down
(z[int]=0) for a class of interesting observables, including the magnetic
susceptibility: this can be done with lexicographic updates but is not possible
with even/odd (z[int]=1) or random (z[int]=2) updates. We are considering the
dynamical critical exponent z[int] for integrated autocorrelations rather than
for the exponential autocorrelation time; this is reasonable because it is the
integrated autocorrelation which determines the cost of a Monte Carlo
computation.
