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Title:Nonperturbative renormalization in classical φ4 theory
Author(s):Hegg, Anthony C
Director of Research:Phillips, Philip
Doctoral Committee Chair(s):Ceperley, David
Doctoral Committee Member(s):Leggett, Anthony; Cooper, Lance
Department / Program:Physics
Discipline:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):renormalization
nonperturbative
phi-4
elliptic
basis
critical point
strong coupling
strongly coupled
Abstract:This is an in-depth study of two analytic nonperturbative renormalization group methods used to study nonrelativistic quartic interacting systems. The model studied is that of classical real scalar φ4 theory. A variety of techniques are used including a rescaling of a nonlinear complete basis, a limit of finite periodic systems, and an analytic calculation of RG equations using a limit of finite systems. Assuming that the truncated forms of the action employed do not change the physics and that standard scaling techniques can be transcribed from more conventional RG approaches to these truncated forms, key results are a new fixed point at strong coupling with exponents ν=2/d and η=2 - d/2 as well as a nonperturbative generation of RG equations and subsequent solution to reduced φ4 theory. A nontrivial critical point for d=3 is identified in this reduced model with ν=4/(1+√41) ≈ 0.540 and η=0.
Issue Date:2016-10-14
Type:Thesis
URI:http://hdl.handle.net/2142/95295
Rights Information:Copyright 2016 Anthony Charles Hegg
Date Available in IDEALS:2017-03-01
Date Deposited:2016-12


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