Existence of Néel order in the S=1 bilinear-biquadratic Heisenberg model via random loops

Abstract

We consider the general spin-1 SU(2) invariant Heisenberg model with a two-body interaction. A random loop model is introduced and relations to quantum spin systems is proved. Using this relation it is shown that for dimensions 3 and above Néel order occurs for a large range of values of the relative strength of the bilinear ($-J_1$) and biquadratic ($-J_2$) interaction terms. The proof uses the method of reflection positivity and infrared bounds. Links between spin correlations and loop correlations are proved.

24 pages, 5 figures

References in corpus (4)

• Some Properties of Correlations of Quantum Lattice Systems in Thermal Equilibrium
• Ferromagnetism, antiferromagnetism, and the curious nematic phase of S=1 quantum spin systems
• Long-range order for the spin-1 Heisenberg model with a small antiferromagnetic interaction
• Validity of spin wave theory for the quantum Heisenberg model

Cited by in corpus (4)

• The free energy in a class of quantum spin systems and interchange processes
• A direct proof of dimerization in a family of SU(n)-invariant quantum spin chains
• Dimerization in quantum spin chains with $O(n)$ symmetry
• Site-monotonicity properties for reflection positive measures with applications to quantum spin systems