Studying of the phase transition in linear sigma model

In this thesis we have investigated systematically the phase structure of the linear sigma model by means of the improved Hatree – Fock approximation, where Goldstone theorem is preserved and self-consistancy of theory is satisfied. Among many results obtained the most remarkable results are in order: 1. We found the chiral phase diagram of the linear sigma model in which the pion condensation was incorporated into consideration. This is the major success of the thesis. Moreover we proved that the chhiral phase transition in chiral limit is second – order if the Goldstone theorem was respected. 2. Taking into account the present of quarks, the phase diagram in - plane has a CEP, this result coincides with prediction of LQCD. 3. The critical temperature of chiral phase transition depends on the length of compactified space – time. Some outlooks: 1. Study phase structure of QCD in Polyakov – LSM in order to study phase structure of QCD in high QCP region. 2. Due to the fact that the critical temperature of phase transition depends on the compactifcation length then the present study might be helpful to explore many physical properties of high temperature superconductors, and, moreover, it can be also applied to studying the Bose - Einstein condensation in (2D + ) - dimensional space.

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