Determination of anisotropy coefficients for SU(3) gauge actions from the integral and matching methods

We use two non-perturbative methods to obtain the anisotropy derivatives of the coupling constants (the anisotropy coefficients) of SU(3) lattice gaug e theory. These coefficients appear in the derivative formulae for the ener gy density and the pressure. We calculate them for the standard Wilson and two improved actions, the (2 x 2) and the Square Symanzik action. Both meth ods lead for all investigated actions to compatible results which are clear ly different from their known asymptotic perturbative limits. With increasi ng beta the limits are however approached in all cases. Our findings strong ly support the equivalence of the integral and derivative methods for the c alculation of energy density and pressure. (C) 2000 Elsevier Science B.V. A ll rights reserved.