# Algorithms for Monte Carlo calculations with fermions

## Abstract

We describe a fermion Monte Carlo algorithm due to Petcher and the present author and another due to Fucito, Marinari, Parisi and Rebbi. For the first algorithm we estimate the number of arithmetic operations required to evaluate a vacuum expectation value grows as N11/mq on an N4 lattice with fixed periodicity in physical units and renormalized quark mass mq. For the second algorithm the rate of growth is estimated to be N8/m2q. Numerical experiments are presented comparing the two algorithms on a lattice of size 24. With a hopping constant K of 0.15 and β of 4.0 we find the number of operations for the second algorithm is about 2.7 times larger than for the first and about 13 000 times larger than for corresponding Monte Carlo calculations with a pure gauge theory. An estimate is given for the number of operations required for more realistic calculations by each algorithm on a larger lattice. © 1985.