G L Celardo | PubMed Health

PubMed2006

Topological nonconnectivity threshold in long-range spin systems.

We demonstrate the existence of a topological disconnection threshold, recently found by Borgonovi [J. Stat. Phys. 116, 1435 (2004)], for generic 1-d anisotropic Heisenberg models interacting with an interparticle potential R(-alpha) when 0<alpha<1(here R is the distance among spins). We also show that alpha if is greater than the embedding dimension then the ratio between the disconnected energy region and the total energy region goes to zero when the number of spins becomes very large. On the other hand, numerical simulations in d=2,3 for the long-range case support the conclusion that such a ratio remains finite for large N values. The disconnection threshold can thus be thought of as a distinctive property of anisotropic long-range interacting systems.

Journal Article↗

PubMed2006

Time scale for magnetic reversal and the topological nonconnectivity threshold.

Anisotropic classical Heisenberg models with all-to-all spin coupling display a topological nonconnectivity threshold (TNT) for any number N of spins. Below this threshold, the energy surface is disconnected in two components with positive and negative total magnetizations, respectively, so that magnetization cannot reverse its sign and ergodicity is broken, even at finite N. Here, we solve the model in the microcanonical ensemble, using a recently developed method based on large deviation techniques, and show that a phase transition is present at an energy higher than the TNT energy. In the energy range between the TNT energy and the phase transition, magnetization changes sign stochastically and its behavior can be fully characterized by an average magnetization reversal time. The time scale for magnetic reversal can be computed analytically, using statistical mechanics. Numerical simulations confirm this calculation and further show that the magnetic reversal time diverges with a power law at the TNT threshold, with a size-dependent exponent. This exponent can be computed in the thermodynamic limit N-->(infinity), by the knowledge of entropy as a function of magnetization, and turns out to be in reasonable agreement with finite numerical simulations. We finally generalize our results to other models: Heisenberg chains with distance-dependent coupling, small 3D clusters with nearest-neighbor interactions, metastable states. We conjecture that the power-law divergence of the magnetic reversal time scale might be a universal signature of the presence of a TNT.

Journal Article↗