Fermion Monte Carlo algorithms

Rough estimates are given for the asymptotic rate of growth of the number of arithmetic operations required by the fermion Monte Carlo algorithm of Petcher and the present author and by the algorithm of Fucito, Marinari, Parisi, and Rebbi. For the first algorithm they find a rate of N/sup 11//m/sub q/ and for the second they obtain N/sup 8//m/sub q//sup 2/ on an N/sup 4/ lattice with renormalized quark mass m/sub q/. Numerical experiments are presented comparing the two algorithms on a 2/sup 4/ lattice. With a hopping constant K of 0.15 and β of 4.0, the number of operations for the second algorithm is about 2.7 times larger than for the first and about 13000 times larger than for corresponding Monte Carlo calculations with a pure gauge theory. An estimate is made of the number of arithmetic operations required by each algorithm for a full calculation of hadron masses