Critical exponents ofO(N)models in fractional dimensions

2014/10/31 by Alessandro Codello, A. Codello, Nicolò Defenu +3 · 69 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic structures and combinatorial models #Algorithm #Black Holes and Theoretical Physics #Computer science #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1103/physrevd.91.105003

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 91(10) (American Physical Society) · 6 pages, 5 figures, reference added

arxiv created 2014/12/04 · openalex publication_date 2015/05/05 · arxiv updated 2015/05/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We compute critical exponents of O(N) models in fractional dimensions between d=2 and 4, and for continuous values of the number of field components N, in this way completing the RG classification of universality classes for these models. These curves represent nonperturbative approximation to the exact results, they respect all the qualitative features expected from such quantities conciliating previously known perturbative results in three dimensions with exact results in two dimensions and giving a strong indication of what could be the exact behavior of such curves. We also report critical exponents for some multicritical universality classes in the cases N\ensuremath≥2 and N=0. Finally, in the large-N limit our critical exponents correctly approach those of the spherical model, allowing us to set N\ensuremath∼100 as the threshold for the quantitative validity of leading order large-N estimates.

Citations

• Existence of Long-Range Order in One and Two Dimensions
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• Critical exponents from the effective average action
• The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results
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Cited by

• Quantum adiabatic cycles and their breakdown
• The nonperturbative functional renormalization group and its applications
• Universal Location of the Yang-Lee Edge Singularity in O(N) Theories
• Topological phase transitions in four dimensions