  We study finite size and temperature XX0 Heisenberg spin chain in weak and
strong coupling regimes. By using an elegant connection of the model to
integrable combinatorics and probability, we explore and interpret a possible
phase structure of the model in asymptotic limit: the limit of large inverse
temperature and size. First, partition function and free energy of the model
are derived by using techniques and results from random matrix models and
nonintersecting Brownian motion. We show that, in the asymptotic limit,
partition function of the model, written in terms of matrix integral, is
governed by the Tracy-Widom distribution. Second, the exact analytic results
for the free energy, which is obtained by the asymptotic analysis of the
Tracy-Widom distribution, indicate a completely new and sophisticated phase
structure of the model. This phase structure consists of second- and
third-order phase transitions. Finally, to shed light on our new results, we
provide a possible interpretation of the phase structure in terms of dynamical
behavior of magnons in the spin chain. We demonstrate distinct features of the
phases with schematic spin configurations which have definite features in each
region of the phase diagram.
