Nonperturbative renormalization in classical φ4 theory

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Hegg, Anthony C

Contributors dc:contributor

• Phillips, Philip
• Ceperley, David
• Leggett, Anthony
• Cooper, Lance

• elliptic
• basis
• critical point
• renormalization
• nonperturbative
• phi-4
• strong coupling
• strongly coupled

Statement dc:rights

• Copyright 2016 Anthony Charles Hegg

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/95295