THE CORRELATION LENGTHS AND THE ORDER OF THE PHASE TRANSITION IN
THREE-DIMENSIONAL Z$_3$ SYMMETRIC MODELS
Sourendu Gupta, A. Irb\"ack, B. Petersson, R.V. Gavai and F. Karsch
Abstract: We present a high statistics Monte Carlo investigation of
three-dimensional Z$_3$ symmetric models, which are related to SU(3)
pure gauge theory at finite temperature. From the finite size scaling
behaviour of bulk properties and the existence of metastable states,
we conclude that these models exhibit a first-order phase transition.
We have also performed detailed correlation length measurements in a
cylindrical geometry with periodic boundary conditions as well as
with a cold wall in the longitudinal direction. The correlation
length, which appears to be independent of the boundary conditions,
becomes very large near the critical point. Nonetheless, our data
suggest that the correlation length develops a discontinuity in the
infinite volume limit.