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Perfect 3-Dimensional Lattice Actions for 4-Dimensional Quantum Field Theories at Finite Temperature

U. Kerres·G. Mack·G. Palma
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Abstract

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bogoliubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for $φ^4$-theory and scalar electrodynamics. The Bałaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here.

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U. Kerres, G. Mack, G. Palma. 1995-06-30. Perfect 3-Dimensional Lattice Actions for 4-Dimensional Quantum Field Theories at Finite Temperature. https://doi.org/10.1016/0550-3213(96)00083-1

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