Tuesday, November 20, 2012

1211.4141 (Daniel Ueltschi)

Quantum Heisenberg models and random loop representations    [PDF]

Daniel Ueltschi
We review random loop representations for the spin-1/2 quantum Heisenberg models, that are due to Toth (ferromagnet) and Aizenman-Nachtergaele (antiferromagnet). These representations can be extended to models that interpolate between the two Heisenberg models, such as the quantum XY model. We discuss the relations between long-range order of the quantum spins and the size of the loops. Finally, we describe conjectures about the joint distribution of the lengths of macroscopic loops, and of symmetry breaking.
View original: http://arxiv.org/abs/1211.4141

No comments:

Post a Comment