1999/09/30 by R. Folk, Yurij Holovatch, Yu. Holovatch +2 · 2 citations
Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Critical exponent #Ising model #Mathematical physics #Mathematics #Monte Carlo method #Perturbation theory (quantum mechanics) #Phase transition #Physics #Quantum mechanics #Renormalization group #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physrevb.61.15114
published as Phys. Rev. B vol. 61, No 22, p. 15114-15129 (2000) · 35 pages, Latex, 9 eps-figures included. The reference list is refreshed and typos are corrected in the 2nd version
openalex publication_date 2000/06/01 · arxiv created 2000/06/16 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05
We present a field-theoretical treatment of the critical behavior of a three-dimensional weakly diluted quenched Ising model. To this end we analyze in the replica limit \stackrel\ensuremath→n0 the five-loop renormalization-group functions of the \ensuremathφ4 theory with O(n)-symmetric and cubic interactions [H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995)]. The minimal subtraction scheme allows one to develop either the √\ensuremathε-expansion series or to proceed within the three-dimensional approach, performing expansions in terms of renormalized couplings. Doing so, we compare both perturbation approaches and discuss their convergence and possible Borel summability. To study the crossover effect we calculate the effective critical exponents. We report resummed numerical values for the effective and asymptotic critical exponents. The results obtained within the three-dimensional approach agree pretty well with recent Monte Carlo simulations. √\ensuremathε expansion does not allow reliable estimates for d=3.