403 research outputs found

    Deformation of a renormalization-group equation applied to infinite-order phase transitions

    Full text link
    By adding a linear term to a renormalization-group equation in a system exhibiting infinite-order phase transitions, asymptotic behavior of running coupling constants is derived in an algebraic manner. A benefit of this method is presented explicitly using several examples.Comment: 6 pages, 5 figures, revtex4, typo corrected, references adde

    Computationally efficient algorithms for the two-dimensional Kolmogorov-Smirnov test

    Get PDF
    Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2^d-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n^2 quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Omega(n^2.lg(n)), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test

    An asymptotic formula for marginal running coupling constants and universality of loglog corrections

    Full text link
    Given a two-loop beta function for multiple marginal coupling constants, we derive an asymptotic formula for the running coupling constants driven to an infrared fixed point. It can play an important role in universal loglog corrections to physical quantities.Comment: 16 pages; typos fixed, one appendix removed for quick access to the main result; to be published in J. Phys.
    corecore