Introduction to statistical field theory: From a toy model to a one-component plasma

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Abstract

� 2015 IOP Publishing Ltd. Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich transformation). We then consider Gaussian-type approximations, wherein correlational contributions enter as harmonic fluctuations around the saddle-point solution. This work focuses on how to arrive at a self-consistent, non-perturbative approximation without recourse to a standard variational construction based on the Gibbs-Bogolyubov-Feynman inequality that is inapplicable to a complex action. To address this problem, we propose a construction based on selective satisfaction of a set of exact relations generated by considering a dual representation of a partition function, in its original and transformed form.
Original languageEnglish
JournalEuropean Journal of Physics
DOIs
Publication statusPublished - 1 Nov 2015
Externally publishedYes

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