Role of Fluctuations in the Linear Sigma Model with Quarks

We study the thermodynamics of the linear sigma model with constituent quarks beyond the mean-field approximation. By integrating out the quark degrees of freedom we derive an effective action for the meson fields which is then linearized around the ground state including field fluctuations. We propose a new method for performing exact averaging of complicated functions over the meson field fluctuations. Both thermal and zero-point fluctuations are considered. The chiral condensate and the effective meson masses are determined self-consistently in a rigorous thermodynamic framework. At zero chemical potential the model predicts a chiral crossover transition which separates two distinct regimes: heavy quarks and light pions at low temperatures, but light quarks and heavy mesons at high temperatures. The crossover becomes a first order phase transition if the vacuum pion mass is reduced from its physical value.