Comparison of the simplicial method with Wilson's lattice gauge theory for U(1) 3

Abstract

In the simplicial version of lattice gauge theory, euclidean path integrals are approximated by tiling spacetime with simplexes and by linearly interpolating the fields throughout each simplex from their values at the vertices. This method is compared with Wilson's lattice gauge theory for U(1) in three dimensions. As a standard of comparison, the exact values of Creutz ratios of Wilson loops in the continuum theory are computed. Monte Carlo computations using the simplicial method give Creutz ratios within a few percent of the exact values for reasonably sized loops at β = 1,2,and10. Similar computations using Wilson's method give ratios that typically differ from the exact values by factors of two or more for 1 ⩽ β ⩽ 3.5 and that have the wrong β dependence. The better accuracy of the simplicial method is due to its use of the action and domain of integration of the exact theory, unaltered apart from the granularity of the simplicial lattice. Data on the action density and the mass gap are also presented.