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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01t435gg93k
Title: Properties of the O(N) Vector Model in Various Dimensions
Properties of the O(N) Vector Model in Various Dimensions
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Authors: Huang, Richard
Advisors: Pufu, Silviu S
Department: Physics
Class Year: 2020
Abstract: In this thesis, we study the O(N) vector model, which is a quantum field theory of N real scalar fields ϕi with a quartic interaction λ4(ϕiϕi)2. We will study the theory in a range of dimensions using two complementary approximation schemes, epsilon expansion in dimensional continuation and the large N approximation. First, we describe various classical solutions of the O(N) model on the sphere Sd for d=6 and 8. Then by computing the determinant of fluctuations about these classical backgrounds, it is possible to provide an alternative method of computing the beta functions in d=6ϵ and d=82ϵ. Finally, we also consider some of the thermodynamic properties of the critical O(N) model by placing the theory on the thermal cylinder S1×Rd1. We find that in the range 2<d<4 and 6<d<8, there exists a real solution for the thermal mass. Interestingly, the leading order contribution to the thermal mass in d=6+ϵ and d=8ϵ is found to have a fractional dependence on ϵ. This is understood by deriving the result diagrammatically and summing over an infinite class of diagrams.
URI: http://arks.princeton.edu/ark:/88435/dsp01t435gg93k
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Physics, 1936-2020

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