University of Illinois Urbana-Champaign

Nonperturbative renormalization in classical φ4 theory

Hegg, Anthony C

Content Files
HEGG-DISSERTATION-2016.pdf

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https://hdl.handle.net/2142/95295

Description

Title
Nonperturbative renormalization in classical φ4 theory
Author(s)
Hegg, Anthony C
Issue Date
2016-10-14
Director of Research (if dissertation) or Advisor (if thesis)
Phillips, Philip
Doctoral Committee Chair(s)
Ceperley, David
Committee Member(s)
  • Leggett, Anthony
  • Cooper, Lance
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2017-03-01T15:46:14Z
Keyword(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.
Graduation Semester
2016-12
Type of Resource
text
Permalink
http://hdl.handle.net/2142/95295
Copyright and License Information
Copyright 2016 Anthony Charles Hegg

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