Critical temperature of Heisenberg models on regular trees, via random loops
Mathematical Physics
2018-11-27 v2 Statistical Mechanics
math.MP
Probability
Abstract
We estimate the critical temperature of a family of quantum spin systems on regular trees of large degree. The systems include the spin- XXZ model and the spin-1 nematic model. Our formula is conjectured to be valid for large-dimensional cubic lattices. Our method of proof uses a probabilistic representation in terms of random loops.
Cite
@article{arxiv.1803.11430,
title = {Critical temperature of Heisenberg models on regular trees, via random loops},
author = {Jakob E. Björnberg and Daniel Ueltschi},
journal= {arXiv preprint arXiv:1803.11430},
year = {2018}
}
Comments
14 pages, to appear in J. Stat. Phys