Hysteresis loop critical exponents in 6-ε dimensions

Hysteresis Loop Critical Exponents in 6 − ǫ Dimensions

The hysteresis loop in the zero–temperature random–field Ising model exhibits a critical point as the width of the disorder increases. Above six dimensions, the critical exponents of this transition, where the “infinite avalanche” first disappears, are described by mean–field theory. We expand the critical exponents about mean–field theory, in 6 − ǫ dimensions, to first order in ǫ. Despite ǫ = ...

Critical exponents from five-loop strong-coupling φ4-theory in 4 − ε dimensions

Recently, one of us [1, 2] has developed a new approach to critical exponents of field theories based on the strong-coupling limit of variational perturbation expansions [3] and [4]3. This limit is relevant for critical phenomena if the renormalization constants are expressed in terms of the unrenormalized coupling constant. The theory was first applied successfully to O(N)symmetric φ4-theories...

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 percolation in high dimensions: critical exponents, finite size scaling and random walks