Critical exponents of theN-vector model

1998/03/31 by Riccardo Guida, R Guida, Jean Zinn-Justin +1 · 32 citations
Physics and Astronomy · #Particle physics theoretical and experimental studies #Quantum and Classical Electrodynamics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1088/0305-4470/31/40/006

published as J.Phys.A31:8103-8121,1998 · TeX Files, 27 pages +2 figures; Some values are changed; references updated

arxiv created 1998/08/31 · openalex publication_date 1998/10/09 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

Recently the series for two renormalization group functions (corresponding to the anomalous dimensions of the fields and ) of the three-dimensional field theory have been extended to next order (seven loops) by Murray and Nickel. We examine the influence of these additional terms on the estimates of critical exponents of the N -vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within the errors of the previous evaluation. Exponents such as (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou-Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published expansions (order ), we have also re-analysed the determination of exponents from the -expansion. The conclusion is that the general agreement between -expansion and three-dimensional series has improved with respect to Le Guillou-Zinn-Justin.

Citations

• Feynman Diagrams to Three Loops in Three Dimensional Field Theory
• Critical exponents from the effective average action
• Finite-Size Scaling in Thin Fe/Ir(100) Layers
• Critical temperatures of the d=3, s=1/2Ising model; the effect of confluent corrections to scaling
• The Magnetization of the 3D Ising Model

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