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On the derivation of effective field theories

Dimo I. Uzunov
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Abstract

A general self-consistency approach allows a thorough treatment of the corrections to the standard mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a new point of view on the effective field theories. The proposed approach can be used for a systematic treatment of fluctuation effects of various length scales and, perhaps, for the development of a new coarse graining procedure. We outline and justify our method by some preliminary calculations. Concrete results are given for the critical temperature and the Landau parameters of the $ϕ^4_d$-theory - the field counterpart of the Ising model. An important unresolved problem of the modern theory of phase transitions - the problem for the calculation of the true critical temperature, is considered within the framework of the present approach. A comprehensive description of the ground state properties of many-body systems is also demonstrated.

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Dimo I. Uzunov. 2004-12-11. On the derivation of effective field theories. https://arxiv.org/abs/hep-lat/0412018

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