Binding of three identical bosons in two dimensions

Qualitative features are discussed for the binding of three identical bosons interacting through pair potentials in two dimensions. Two special cases, known to yield pathologies in three dimensions, are examined using the Faddeev equation for the bound states. The Thomas effect does not occur: in the model which is treated, the trimer binding energy is finite for a zero-range force with a finite dimer energy. The Efimov effect can only occur under more restrictive conditions than in three dimensions: the number of bound trimer states is finite at the dimer threshold for a range of potential models. The trimer ground-state energy is determined as a function of the coupling constant for a simple model, and variational results for loosely bound Lennard-Jones trimers are shown to reflect a general trend found for the model.