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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Physics of the solid state 42 (2000), S. 2151-2158 
    ISSN: 1063-7834
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The paper is devoted to the calculation of renormalization-group (RG) functions in the O(n)-symmetry two-dimensional model of the λϕ 4 type in the five-loop approximation and to an analysis of the critical behavior of systems described by this model. Five-loop expansions for the β function and the critical indices are determined in bulk theory. They are summed up using the Padé-Borel and Padé-Borel-Le Roy methods, making it possible to optimize the summation procedure and to estimate the accuracy of the obtained numerical values. It is shown that in the Ising (n=1) case, as well as in other cases, the inclusion of the five-loop contribution to the β function displaces the coordinate of the Wilson fixed point only insignificantly, leaving it outside the interval formed by the results of computations on lattices; even “spreads” of the error in the renormalization group and lattice estimates do not overlap. This discrepancy is attributed to the effect of the nonanalytic com-ponent of the β function, which cannot be determined in perturbation theory. A computation of critical indices proves that, although the inclusion of the five-loop terms in the corresponding RG expansion slightly improves the concordance with the exact results, the nonanalytic contributions are apparently also significant in this case.
    Type of Medium: Electronic Resource
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