Linear sigma model at finite temperature

Abstract

The chiral phase transition is investigated within the framework of thermal field theory using the O(N) linear sigma model as an effective theory. We calculate the thermal effective potential by using the Cornwall-Jackiw-Tomboulis formalism of composite operators. The thermal effective potential is calculated for N=4 involving as usual the sigma and the three pions, and in the large-N approximation involving N-1 pion fields. In both cases, the system of the resulting gap equations for the thermal effective masses of the particles has been solved numerically, and we have investigated the evolution of the effective potential. In the N=4 case, there is indication of a first-order phase transition, while in the large N approximation the phase transition appears as second-order. In this analysis, we have ignored quantum fluctuations and have used the imaginary time formalism for calculations. We have extended our calculation in order to include the full effect of two loops in the calculation of the effective potential. In this case, the effective masses are momentum dependent. In order to perform the calculations, we found the real time formalism to be convenient. We have calculated the effective masses of pions at the low-temperature phase and we found a quadratic dependence on temperature, in contrast to the Hartree case, where the mass is proportional to temperature. The sigma mass was investigated in the presence of massive pions, and we found a small deviation compared to the Hartree case. In all cases, the system approaches the behaviour of the ideal gas at the high temperature limit.

33 pages, 40 eps figures, based on PhD thesis submitted to Manchester University in Oct 2000

References in corpus (36)

• The Effective Potential and First-Order Phase Transitions: Beyond Leading Order
• Static and Dynamic Critical Phenomena at a Second Order QCD Phase Transition
• Resummation in a Hot Scalar Field Theory
• The Three-Loop Free Energy for Pure Gauge QCD
• The Three-Loop Free Energy for High-Temperature QED and QCD with Fermions
• Optimized Perturbation Theory at Finite Temperature
• Self-consistent Improvement of the Finite Temperature Effective Potential
• Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries
• Propagation of Cool Pions
• Chiral symmetry restoration in linear sigma models with different numbers of quark flavors
• Linear sigma model and chiral symmetry at finite temperature
• Forming Disoriented Chiral Condensates through Fluctuations
• Thermal Effective Potential of the O(N) Linear sigma Model
• Effective Potential of O(N) Linear Sigma Model at Finite Temperature
• Statistical Properties of the Linear Sigma Model
• Mean-field treatment of the linear sigma model in dynamical calculations of DCC observables
• On the CJT Formalism in Multi-Field Theories
• The Chiral Fermion Meson Model at Finite Temperature
• Chiral Phase Transition at Finite Temperature in the Linear Sigma Model
• Introduction to Thermal Field Theory
• On the Analytic Structure of the Self-Energy for Massive Gauge Bosons at Finite Temperature
• Finite temperature spectral functions of the linear O(N)-model at large N applied to the $\pi -\sigma$ system
• Self-consistently Improved Finite Temperature Effective Potential for Gauge Theories
• Study of the O(N) linear sigma model at finite temperature using the 2PPI expansion
• A 2 Loop 2PPI Analysis of $\lambda {\varphi }^4$ at Finite Temperature
• Second sheet $\sigma$ pole and the threshold enhancement of the spectral function in the scalar-isoscalar meson-sector
• Nonequilibrium evolution in scalar O(N) models with spontaneous symmetry breaking
• Soft Modes, Resonances and Quantum Transport
• A Re-examination of the Path Ordered Approach to Real Time Thermal Field Theory
• Pion propagation in the linear sigma model at finite temperature
• Disoriented chiral condensate formation from tubes of hot quark plasma
• Topics in Finite Temperature Field Theory
• Pion dispersion relation at finite temperature in the linear sigma model from chiral Ward identities
• Roles of Chiral Symmetry and the Sigma Meson in Hadron and Nuclear Physics
• Thermal effective potential of the linear sigma model
• Chiral Ward identities and pion propagation at finite temperature in the linear sigma model