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 $\beta =0\mathrm{}$ (strong coupling) to $\beta =6.0\mathrm{}$ (in the scaling region), and for lattice sizes up to ${V=64\mathrm{}}^3.$ In the limit of large lattice volume we observe, in all cases, a gluon propagator decreasing for momenta smaller than a constant value $p_{\mathrm{dec}}.$ From our data we estimate $p_{\mathrm{dec}}\approx 350\hspace{0.5em}\mathrm{MeV}.$ 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.