Topological Non--connectivity Threshold in long-range spin systems

Abstract

We demonstrate the existence of a topological disconnection threshold, recently found in Ref. \cite{JSP}, for generic $1-d$ anisotropic Heisenberg models interacting with an inter--particle potential $R^{-\alpha }$ when $0<\alpha <1$ (here $R$ is the distance among spins). We also show that if $\alpha$ is greater than the embedding dimension $d$ 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 $\alpha <d$ support the conclusion that such a ratio remains finite for large $N$ values. The disconnection threshold can thus be thought as a distinctive property of anisotropic long-range interacting systems.

submitted to PRE

References in corpus (6)

• Inequivalence of ensembles in a system with long range interactions
• Phase transitions and topology changes in configuration space
• Broken Ergodicity in classically chaotic spin systems
• The Non--Ergodicity Threshold: Time Scale for Magnetic Reversal
• Quantum Signatures of The Classical Disconnection Border
• Domain-wall profile in the presence of anisotropic exchange interactions: Effective on-site anisotropy

Cited by in corpus (10)

• Thermodynamics and dynamics of systems with long-range interactions
• Cooperative shielding in many-body systems with long-range interaction
• Phase space gaps and ergodicity breaking in systems with long range interactions
• Quasistationarity in a long-range interacting model of particles moving on a sphere
• Relaxation dynamics of stochastic long-range interacting systems
• Breakdown of the Quantum Distinction of Regular and Chaotic Classical Dynamics in Dissipative Systems
• Nosé-Hoover and Langevin thermostats do not reproduce the nonequilibrium behavior of long-range Hamiltonians
• Dynamics of random dipoles : chaos {\it vs} ferromagnetism
• Magnetic Reversal Time in Open Long Range Systems
• Enhancement of magnetic anisotropy barrier in long range interacting spin systems