
Published online:
01 January 2010
Published in print:
05 July 2007
Online ISBN:
9780191711107
Print ISBN:
9780199227198
Contents
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10.1 Critical Hamiltonian and perturbative expansion 10.1 Critical Hamiltonian and perturbative expansion
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10.2 Feynman diagrams at one-loop order 10.2 Feynman diagrams at one-loop order
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10.3 Fixed point and critical behaviour 10.3 Fixed point and critical behaviour
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10.3.1 The two-point function 10.3.1 The two-point function
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10.3.2 The four-point function 10.3.2 The four-point function
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10.3.3 Fixed point 10.3.3 Fixed point
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10.3.4 The field dimension to order e 2 10.3.4 The field dimension to order e 2
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Field dimension: Correction to the Gaussian value. Field dimension: Correction to the Gaussian value.
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10.4 Critical domain 10.4 Critical domain
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10.4.1 Two-point function 10.4.1 Two-point function
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10.4.2 Renormalization group 10.4.2 Renormalization group
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10.4.3 Two-point function: Scaling behaviour in the critical domain 10.4.3 Two-point function: Scaling behaviour in the critical domain
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10.5 Models with O(N) orthogonal symmetry 10.5 Models with O(N) orthogonal symmetry
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10.6 Renormalization group near dimension 4 10.6 Renormalization group near dimension 4
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10.6.1 Critical Hamiltonian and RGE 10.6.1 Critical Hamiltonian and RGE
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10.6.2 Critical domain 10.6.2 Critical domain
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Equations in a field or below T c. Equations in a field or below T c.
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Specific heat. Specific heat.
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10.7 Universal quantities: Numerical results 10.7 Universal quantities: Numerical results
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Chapter
10 Perturbative renormalization group: Explicit calculations
Get access
Pages
243–266
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Published:July 2007
Cite
Zinn-Justin, Jean, 'Perturbative renormalization group: Explicit calculations', Phase Transitions and Renormalization Group, Oxford Graduate Texts (Oxford , 2007; online edn, Oxford Academic, 1 Jan. 2010), https://doi.org/10.1093/acprof:oso/9780199227198.003.0010, accessed 3 May 2025.
Abstract
This chapter uses the assumptions introduced in Chapter 9 to show that it is indeed possible to find a non-Gaussian fixed point in dimension d = 4 - e, both in models with reflection and rotation symmetries. It briefly introduces the field theory methods that will be described more thoroughly in the following chapters. Finally, it presents a selection of numerical results concerning critical exponents and some universal amplitude ratios.
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