The thermal coupling constant and the gap equation in the $\lambda {\varphi }_D^4$ model

Abstract

By the concurrent use of two different resummation methods, the composite operator formalism and the Dyson-Schwinger equation, we re-examinate the behavior at finite temperature of the O(N)-symmetric $\lambda {\varphi }^4$ model in a generic D-dimensional Euclidean space. In the cases D=3 and D=4, an analysis of the thermal behavior of the renormalized squared mass and coupling constant are done for all temperatures. It results that the thermal renormalized squared mass is positive and increases monotonically with the temperature. The behavior of the thermal coupling constant is quite different in odd or even dimensional space. In D=3, the thermal coupling constant decreases up to a minimum value diferent from zero and then grows up monotonically as the temperature increases. In the case D=4, it is found that the thermal renormalized coupling constant tends in the high temperature limit to a constant asymptotic value. Also for general D-dimensional Euclidean space, we are able to obtain a formula for the critical temperature of the second order phase transition. This formula agrees with previous known values at D=3 and D=4.

arXiv comment23 pages, 4 figures

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Cited by in corpus (15)

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• High Temperature Resummation in the Linear $\delta$-Expansion
• Boundary dependence of the coupling constant and the mass in the vector N-component $(\lambda {\varphi }^4{)}_D$ theory
• Finite Size Effects in Thermal Field Theory
• First-order phase transitions in superconducting films: A Euclidean model
• Large-N $\beta$-function for superconducting films in a magnetic field
• Spontaneous symmetry breaking in replica field theory
• Disordered $\lambda {\phi }^4+\rho {\phi }^6$ Landau-Ginzburg model
• A note on the infrared behavior of the compactified Ginzburg--Landau model in a magnetic field
• Multiplicative Noise in Euclidean Schwarzschild Manifold
• Restoration of a Spontaneously Broken Symmetry in an Euclidean Quantum $\lambda {\phi }_{d+1}^4$ model with Quenched Disorder
• Disordered Bose-Einstein condensate in hard walls trap
• A minimal size for granular superconductors
• Finite-Size Effects in Disordered $\lambda {\varphi }^4$ Model
• The Composite Operator (CJT) Formalism in the $(\lambda {\varphi }^4+\eta {\varphi }^6{)}_{D=3}$ Model at Finite Temperature