We show how to combine Kesten’s scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov’s proof of Cardy’s formula, in order to determine the existence and value of critical exponents associated to percolation on the triangular lattice.

The staircase model is a recently discovered [5] one-parameter family of integrable two-dimensional continuum field theories. We analyze the novel critical behavior of this model, seen as a perturbation of a minimal conformal theory Mp: the leading thermodynamic singularities are simultaneously governed by all fixed points Mp,Mp−1, . . . ,M3. The exponents of the magnetic susceptibility and the...

We analyze the behavior of the spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents t and m5d/D , recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For the one-dimensional anisotropic Bak-Sneppen model, we derive an exact equation for the distribution of avalanche spatial sizes, and extract t...

With Monte Carlo simulations, we systematically investigate the depinning phase transition in the two-dimensional driven random-field clock model. Based on the short-time dynamic approach, we determine the transition field and critical exponents. The results show that the critical exponents vary with the form of the random-field distribution and the strength of the random fields, and the roughe...

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 ...

We present the pseudo-ǫ expansions (τ -series) for the critical exponents of a λφ4 threedimensional O(n)-symmetric model obtained on the basis of six-loop renormalization-group expansions. Concrete numerical results are presented for physically interesting cases n = 1, n = 2, n = 3 and n = 0, as well as for 4 ≤ n ≤ 32 in order to clarify the general properties of the obtained series. The pseudo...