THE ANISOTROPIC WILSON GAUGE ACTION

Anisotropic lattices, with a temporal lattice spacing smaller than the spatial one, allow precision Monte Carlo calculations of problems tha t are difficult to study otherwise: heavy quarks, glueballs, hybrids, and high temperature thermodynamics, for example. We here perform the first step required for such studies with the (quenched) Wilson gauge action, namely, the determination of the renormalized anisotropy xi as a function of the bare anisotropy xi(0) and the coupling. By, essenti ally, comparing the finite-volume heavy quark potential where the quar ks are separated along a spatial direction with that where they are se parated along the time direction, we determine the relation between xi and xi(0) to a fraction of 1% for weak and to 1% for strong coupling. We present a simple parameterization of this relation for 1 less than or equal to xi less than or equal to 6 and 5.5 less than or equal to beta less than or equal to infinity, which incorporates the known one- loop result and reproduces our non-perturbative determinations within errors. Besides solving the problem of how to choose the bare anisotro pies if one wants to take the continuum limit at Axed renormalized ani sotropy, this parameterization also yields accurate estimates of the d erivative partial derivative xi(0)/partial derivative xi needed in the rmodynamic studies. (C) 1998 Elsevier Science B.V.