  We consider the 2D SU(N) principal chiral model and discuss a vortex
condensation mechanism which could explain the existence of a non-zero mass gap
at arbitrarily small values of the coupling constant. The mechanism is an
analogue of the vortex condensation mechanism of confinement in 4D non-Abelian
gauge theories. We formulate a sufficient condition for the mass gap to be
non-vanishing in terms of the behaviour of the vortex free energy. The SU(2)
model is studied in detail. In one dimension we calculate the vortex free
energy exactly. An effective model for the center variables of the spin
configurations of the 2D SU(2) model is proposed and the Z(2) correlation
function is derived in this model. We define a Z(2) mass gap in both the full
and effective model and argue that they should coincide whenever the genuine
mass gap is non-zero. We show via Monte-Carlo simulations of the SU(2) model
that the Z(2) mass gap reproduces the full mass gap with perfect accuracy. We
also test this mechanism in the positive link model which is an analogue of the
positive plaquette model in gauge theories and find excellent agreement between
the full and the Z(2) mass gap.
