Critical Exponents in Zero 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 for the SC-Model in the Zero Sector

In this paper, we continue our investigation of a one-dimensional, twocomponent, quantum many-body system in which like particles interact with a pair potential s(s + 1)/sinh(r), while unlike particles interact with a pair potential −s(s + 1)/cosh(r). For an equal number of particles of the two components, the ground state for s > 0 corresponds to an antiferromagnet/insulator. Excitations consi...

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