λ-transition in low dimensional systems with SU_q(2) symmetry

Abstract

We show that $SU_q(2)$ invariant systems in one and two dimensions exhibit Bose-Einstein condensation for $q >1$. For these systems there is a $λ$-transition at the critical temperature. The critical temperature and the gap in the heat capacity increase more rapidly for small deviations from the standard value $q=1$, and they become approximately constant for large values of $q$. For low temperatures and $q>1$ the entropy is lower than the entropy of an ideal Bose gas.