Precise determination of critical exponents and equation of state by field theory methods

2000/02/16 by J. Zinn-Justin, J Zinn-Justin · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Theoretical and Computational Physics #hep-th

paper · pdf · doi:10.1016/s0370-1573(00)00126-5

published as Phys.Rept.344:159-178,2001 · 23 pages, tex, private macros, one figure

arxiv created 2000/02/16 · openalex publication_date 2001/04/01 · arxiv updated 2011/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Renormalization group, and in particular its Quantum Field Theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the methods, based on renormalized phi⁴₃ quantum field theory and renormalization group, which have led to a precise determination of critical exponents of the N-vector model (R. Guida and J. Zinn-Justin, J. Phys. A31 (1998) 8103. cond-mat/9803240). and of the equation of state of the 3D Ising model (R. Guida and J. Zinn-Justin, Nucl. Phys. B489 [FS] (1997) 626, hep-th/9610223.). These results are among the most precise available probing field theory in a non-perturbative regime.

Citations

• The renormalization group and the ε expansion
• Four-point renormalized coupling constant and Callan-Symanzik β-function in O(N) models
• Critical exponents from the effective average action
• Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching
• 3D Ising model: the scaling equation of state
• Critical exponents of theN-vector model
• The Magnetization of the 3D Ising Model

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