Lees, Benjamin (2016) Existence of Néel order in the S=1 bilinear-biquadratic Heisenberg model via random loops. Communications in Mathematical Physics, 347 (1). pp. 83-101. ISSN 0010-3616.

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Abstract

We consider the general spin-1 SU(2) invariant Heisenberg model with a two-body interaction. A random loop model is introduced and relation 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 (−J1) and biquadratic (−J2) interaction terms. The proof uses the method of reflection positivity and infrared bounds. Links between spin correlations and loop correlations are proved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Heisenberg uncertainty principle, Loops (Group theory)
Journal or Publication Title:	Communications in Mathematical Physics
Publisher:	Springer
ISSN:	0010-3616
Official Date:	October 2016
Dates:	Date Event October 2016 Published 24 May 2016 Available 7 April 2016 Accepted
Volume:	347
Number:	1
Number of Pages:	19
Page Range:	pp. 83-101
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	15 September 2016
Date of first compliant Open Access:	15 September 2016
Funder:	Engineering and Physical Sciences Research Council (EPSRC), University of Warwick
Grant number:	EP/HO23364/1 (EPSRC)

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