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Journal of Statistical Physics

Computation of the Breakdown of Analyticity in Statistical Mechanics Models: Numerical Results and a Renormalization Group Explanation

Renato Calleja, Rafael de la Llave

Published Nov 3, 2010• 24 citations
Publisher
DOI
10.1007/s10955-010-0085-7

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This dissertation focuses on theoretical studies of relativistic Bose-Einstein condensation (BEC).Based on the complex scalar field theory, which serves as a fundamental model for relativistic BEC, we provide a detailed explanation of the analyses using the functional renormalization group (FRG), including both its formalism and the underlying physics.We also present the numerical implementation of the FRG flow equation and the results obtained from it, as well as the derivations of various related equations.Although previous studies rely on approaches that are not well justified, we develop a novel and physically consistent FRG framework.In this framework, we impose a condition on the FRG flow equation, analogous to that in the non-interacting case.By solving the equation under this condition, we find that quantum fluctuations significantly affect the phase transition of relativistic BEC in the strong coupling regime.We further investigate the dependence of the condensate on spatial dimensions, and in particular, confirm that the FRG analysis is consistent with the Mermin-Wagner theorem from both numerical and analytical perspectives.These results contribute to the development of the theoretical foundation of the FRG, and uncover an aspect of relativistic BEC under non-perturbative interactions and for various spatial dimensions.