Critical Exponents in Three Dimensions

Critical Exponents and Dimensions for Elliptic Equations

Polyharmonic Dirichlet Problems: Positivity, Critical Exponents and Critical Dimensions

In this summary we want to present the main results which are contained in the author’s “Habilitationsschrift” (dissertation). It has been written in German and has been submitted to the Faculty of Mathematics and Physics of the University of Bayreuth. Moreover we want to comment on these results, sketch some of the ideas how to prove them and give some background information. For the reader’s ...

Critical exponents of the superfluid-Bose-glass transition in three dimensions.

Recent experimental and numerical studies of the critical-temperature exponent ϕ for the superfluid-Bose-glass universality in three-dimensional systems report strong violations of the key quantum critical relation, ϕ=νz, where z and ν are the dynamic and correlation-length exponents, respectively; these studies question the conventional scaling laws for this quantum critical point. Using Monte...

Fast-Convergent Resummation Algorithm and Critical Exponents of φ-Theory in Three Dimensions

Abstract We develop an efficient algorithm for evaluating divergent perturbation expansions of field theories in the bare coupling constant gB for which we possess a finite number L of expansion coefficients plus two more informations: The knowledge of the large-order behavior proportional to (−α)kk!kβgk B, with a known growth parameter α, and the knowledge of the approach to scaling being of t...

20 Critical Exponents from Other Expansions 20.1 Sixth-order Expansions in Three Dimensions

It is useful to compare the results obtained so far with other approaches to the critical exponents. One is a similar field-theoretic approach based on perturbation expansions of φ 4-theories. But instead of working in D = 4−ε dimensions and continuing the results to ε = 1 to obtain critical exponents in the physical dimension D = 3, perturbation expansions can be derived directly in three dime...