scholarly journals Phase transition for loop representations of quantum spin systems on trees

2018 ◽  
Vol 59 (11) ◽  
pp. 113302 ◽  
Author(s):  
Volker Betz ◽  
Johannes Ehlert ◽  
Benjamin Lees
1990 ◽  
Vol 68 (12) ◽  
pp. 1410-1418 ◽  
Author(s):  
D. D. Betts ◽  
S. Miyashita

We consider the zero-temperature properties of four different spin 1/2 models on two-dimensional lattices: the XY ferromagnet, the XY antiferromagnet, the Heisenberg antiferromagnet, and the Dzyaloshinsky–Moriya models. Most of this article is a review of previously published work, but a few previously unpublished results are included. The relation between three of the models on bipartite lattices is described. The properties of the XY ferromagnet in two dimensions, especially those derived from extrapolation of finite lattice results, are reviewed. A numerical factor by which spin-wave and finite-lattice estimates of the long-range order parameter differ is discussed. For frustrated models on the triangular lattice the possibility of a chirality phase transition instead of, or in addition to, a magnetic phase transition is considered.


2006 ◽  
Vol 269 (3) ◽  
pp. 611-657 ◽  
Author(s):  
Marek Biskup ◽  
Lincoln Chayes ◽  
Shannon Starr

2000 ◽  
Vol 284-288 ◽  
pp. 1625-1626 ◽  
Author(s):  
Y Ajiro ◽  
T Asano ◽  
Y Inagaki ◽  
J.P Boucher ◽  
S Luther ◽  
...  

2012 ◽  
Vol 14 (9) ◽  
pp. 093039 ◽  
Author(s):  
Florian Fröwis ◽  
Wolfgang Dür

1998 ◽  
Vol 31 (8) ◽  
pp. 2045-2056 ◽  
Author(s):  
Adam W Majewski ◽  
Robert Olkiewicz ◽  
Boguslaw Zegarlinski

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