Surface scaling behavior of isotropic Heisenberg systems: Critical exponents, structure factor, and profiles

eb 2 00 1 Dynamic surface critical behavior of isotropic Heisenberg ferromagnets

The effects of free surfaces on the dynamic critical behavior of isotropic Heisenberg ferromagnets are studied via phenomenological scaling theory, field-theoretic renormalization group tools, and high-precision computer simulations. An appropriate semi-infinite extension of the stochastic model J is constructed, the boundary terms of the associated dynamic field theory are identified, its reno...

Critical exponents of the Heisenberg spin chain.

ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

Finite-size scaling and critical exponents in critical relaxation.

We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are reported, based on the finite size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent z is extracted i...

Scaling Limit and Critical Exponents for Two-Dimensional Bootstrap Percolation

Consider a cellular automaton with state space {0, 1}Z2 where the initial configuration ω0 is chosen according to a Bernoulli product measure, 1’s are stable, and 0’s become 1’s if they are surrounded by at least three neighboring 1’s. In this paper we show that the configuration ωn at time n converges exponentially fast to a final configuration ω̄, and that the limiting measure corresponding to...