English

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-12\frac12 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.

Keywords

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