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We have implemented a procedure, which we call extremization, that deterministically evolves a configuration of lattice field theory towards a solution of the lattice field equations. The solution obtained need not be a local minimum of the action. A Fourier accelerated version of the algorithm is used in three-dimensional SU (2) lattice gauge theory to generate saddle-point solutions of the lattice field equations from Monte Carlo generated lattices. We find that the string tension persists under moderate extremization, during which the average action decreases by a factor of about 100 and the lattices show localized peaks in the action density, as seen in cooling. Continued extremization removes the plateau in the Creutz ratios.

Configurations of SU(2) lattice gauge theory in three dimensions are generated by Monte Carlo and then cooled. These cooled configurations give area law behavior for Wilson loops (for single configurations and averages over all configurations), are composed of fields which are smooth (in Landau gauge) functions, and are seen to contain localized lumps of large action connected by tails of small action. Further cooling of only the tail regions tends to give well defined plateaus in the Creutz ratios and sometimes leads to plateaus even if the lumps undergo independent global color rotations.