Self consistent renormalization theory of itinerant ferromagnets is used to calculate the Curie temperature of clusters down to approximately 100 atoms in size. In these clusters the electrons responsible for the magnetic properties are assumed to be
(weakly) itinerant. It is shown that the Curie temperature can be larger than in the bulk. The effect originates from the phenomenon of level repulsion in chaotic quantum systems, which suppresses spin fluctuations. Since the latter destroy the magnetic order the resulting Curie temperature increases, contrary to expectations of the naive Stoner picture. The calculations are done assuming that the energy levels of the cluster are described by the Gaussian Orthogonal Ensemble of random matrix theory.
The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D me
mbranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 AA which is compatible with experimental findings (50-100 AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.
