Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus $ε^{1/2}$-Expansion

Details Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus $ε^{1/2}$-Expansion Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus $ε^{1/2}$-Expansion

1999-09-08

arxiv.org/abs/cond-mat/9909121v2

Phys. Rev. B vol. 61, No 22, p. 15114-15129 (2000)

Physics

Condensed Matter

35 pages, Latex, 9 eps-figures included. The reference list is refreshed and typos are corrected in the 2nd version

Scientific paper

10.1103/PhysRevB.61.15114

We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in a replica limit n=0 5-loop renormalization group functions of the $\phi^4$-theory with O(n)-symmetric and cubic interactions (H.Kleinert and V.Schulte-Frohlinde, Phys.Lett. B342, 284 (1995)). The minimal subtraction scheme allows to develop either the $\epsilon^{1/2}$-expansion series or to proceed in the 3d 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 providing a local measure for the degree of singularity of different physical quantities in the critical region. We report resummed numerical values for the effective and asymptotic critical exponents. Obtained within the 3d approach results agree pretty well with recent Monte Carlo simulations. $\epsilon^{1/2}$-expansion does not allow reliable estimates for d=3.

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