Analysis of a Fully Packed Loop Model Arising in a Magnetic Coulomb Phase

L. D. C. Jaubert (1) , M. Haque (1) , R. Moessner (1)

1 MPI-PKS - Max Planck Institute for the Physics of Complex Systems

The Coulomb phase of spin ice, and indeed the Ic phase of water ice, naturally realize a fully packed two-color loop model in 3D. We present a detailed analysis of the statistics of these loops: we find loops spanning the system multiple times hosting a finite fraction of all sites while the average loop length remains finite. We contrast the behavior with an analogous 2D model. We connect this body of results to properties of polymers, percolation and insights from Schramm-Loewner evolution processes. We also study another extended degree of freedom, called worms, which appear as “Dirac strings” in spin ice. We discuss implications of these results for the efficiency of numerical cluster algorithms, and address implications for the ordering properties of a broader class of magnetic systems, e.g., with Heisenberg spins, such as CsNiCrF6 or ZnCr2O4.

Domaines: Mécanique statistique [cond-mat.stat-mech]

L. D. C. Jaubert, M. Haque, R. Moessner. Analysis of a Fully Packed Loop Model Arising in a Magnetic Coulomb Phase. Physical Review Letters, 2011, 107, pp.177202. ⟨10.1103/PhysRevLett.107.177202⟩. ⟨hal-01541713⟩