a Study of the Chiral Phase Transition in the Non-Linear Sigma Model

The finite temperature chiral phase transition is studied using the three dimensional non-linear sigma model. Numerical simulations with the U(N) times U(N) and SU(N) times SU(N) flavor symmetries for both two and three flavors were examined to determine the order of the phase transition. The data from the simulations in the appropriate limits was verified with calculations from the strong and weak coupling expansions. A variety of numerical techniques, including metastability analysis, reduced cumulant of the energy, and finite sized scaling were employed to determine the transition for both flavors using the U(N) times U(N) and SU(N) times SU(N) flavor symmetries. The results of these simulations for the finite temperature chiral phase transition and chiral symmetry restoration are summarized, and a discussion of the implications for heavy-ion collider physics and cosmology is presented.