Critical temperature of Heisenberg models on regular trees, via random loops

Abstract

We estimate the critical temperature of a family of quantum spin systems on regular trees of large degree. The systems include the spin-$\frac{1}{2}$ 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.

arXiv comment14 pages, to appear in J. Stat. Phys

References in corpus (8)

• Geometric Aspects of Quantum Spin States
• Critical temperature and the transition from quantum to classical order parameter fluctuations in the three-dimensional Heisenberg antiferromagnet
• Random loop representations for quantum spin systems
• Infinite cycles in the random stirring model on trees
• A numerical study of the 3D random interchange and random loop models
• Decay of transverse correlations in quantum Heisenberg models
• Phase transition for loop representations of Quantum spin systems on trees
• Critical parameter of random loop model on trees

Cited by in corpus (4)

• The interchange process with reversals on the complete graph
• Phase transition for loop representations of Quantum spin systems on trees
• Critical Parameters for Loop and Bernoulli Percolation
• On a class of orthogonal-invariant quantum spin systems on the complete graph