The Large N Limit and the High Temperature Phase Transition for the ϕ^4 Theory

Abstract

We study, with various methods (standard large N evaluation of the functional integral for the effective potential, solution of the Schwinger-Dyson equations), the high temperature phase transition for the $N$-component ${\varphi }^4$ theory in the large $N$ limit. Our results fully confirm a previous investigation of the problem, for arbitrary $N$, with the method of the average potential which employs renormalization group ideas. The phase transition is of the second order with an effectively three-dimensional critical behaviour. }

DESY-93-004, 23 pages, 2 figures available by fax upon request

References in corpus (2)

• Exact evolution equation for the effective potential
• On the phase transition in the scalar theory

Cited by in corpus (40)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
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• Analytical Solutions of Exact Renormalization Group Equations
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• A Consistent Calculation of Bubble-Nucleation Rates
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• Boundary dependence of the coupling constant and the mass in the vector N-component $(\lambda {\varphi }^4{)}_D$ theory
• High Temperature Phase Transition in Two-Scalar Theories
• Fractals at T=Tc due to instanton-like configurations
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• The Fractal Geometry of Critical Systems
• Dimensional Crossover and Effective Exponents
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• The thermal coupling constant and the gap equation in the $\lambda {\varphi }_D^4$ model
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• Phase transition in scalar ${\varphi }^4$-theory beyond the super daisy resummations
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• Nonperturbative Contributions to the Hot Electroweak Potential and the Crossover
• A strongly first order electroweak phase transition from strong symmetry-breaking interactions
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• Sphaleron Effects Near the Critical Temperature
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• Comparison of Renormalization-Group and Lattice Studies of the Electroweak Phase Transition
• Polchinski ERG Equation in O(N) Scalar Field Theory
• High temperature phase of QCD
• ERG and Schwinger-Dyson Equations - Comparison in formulations and applications --
• Flow of the Coarse Grained Free Energy for Crossover Phenomena
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• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
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