Nonperturbative renormalization in classical φ4 theory

Hegg, Anthony C

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

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

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

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

Copyright and License Information

Copyright 2016 Anthony Charles Hegg

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