The Local Hybrid Monte Carlo Algorithm for Free Field Theory: Reexamining Overrelaxation

We analyze the autocorrelations for the Local Hybrid Monte Carlo algorithm [1] in the context of free field theory. In this case this is just Adler’s overrelaxation algorithm [2]. 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 (zint = 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 (zint = 1) or random (zint = 2) updates. We are considering the dynamical critical exponent zint 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.