Infrared behavior of the gluon propagator in the lattice Landau gauge: The three-dimensional case

We evaluate numerically the three-momentum-space gluon propagator in the lattice Landau gauge, for three-dimensional pure-SU(2) lattice gauge theory with periodic boundary conditions. Simulations are done for nine different values of the coupling beta, from beta = 0 (strong coupling) to beta=6.0 (in the scaling region), and for lattice sizes up to V=64(3). In the limit of large lattice volume we observe, in all cases, a gluon propagator decreasing for momenta smaller than a constant value p(dec). From our data we estimate p(dec) approximate to 350 MeV. The result of a gluon propagator decreasing in the infrared limit has a straightforward interpretation as resulting from the proximity of the so-called first Gribov horizon in the infrared directions. [S0556-2821(99)04713-X].