The LHMC Algorithm for Free Field Theory: Reexamining Overrelaxation

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.