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We attempt the numerical construction of an effective action in threedimensions for Ising spins which represent the Wilson lines in thefour-dimensional SU(3) gauge theory at finite temperature. For eachconfiguration of the gauge theory, each spin is determined by averaging theWilson lines over a small neighborhood and then projecting the average to +/-1according to whether the neighborhood is ordered or disordered. The effectiveIsing action, determined via the lattice Schwinger-Dyson equations, containseven (two-spin) and odd (one- and three-spin) terms with short range. We findthat the truncation to Ising degrees of freedom produces an effective actionwhich is discontinuous across the gauge theory's phase transition. Thisdiscontinuity may disappear if the effective action is made more elaborate.Comment: 12 pages, revtex, including 2 Postscript figures; conclusions have  changed slightly to conform to the theorem of Van Enter, Fernandez, and Sokal  on the continuity of RG map

Ising description of the transition region in SU(3) gauge theory at finite temperature