Ferromagnetism, antiferromagnetism, and the curious nematic phase of S=1 quantum spin systems.

@article{Ueltschi2015FerromagnetismAA,
  title={Ferromagnetism, antiferromagnetism, and the curious nematic phase of S=1 quantum spin systems.},
  author={Daniel Ueltschi},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={91 4},
  pages={
          042132
        }
}
  • D. Ueltschi
  • Published 9 June 2014
  • Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We investigate the phase diagram of S=1 quantum spin systems with SU(2)-invariant interactions, at low temperatures and in three spatial dimensions. Symmetry breaking and the nature of extremal states can be studied using random loop representations. The latter confirm the occurrence of ferro- and antiferromagnetic transitions and the breaking of SU(3) invariance. And they reveal the peculiar nature of the nematic extremal states which minimize ∑(x)(S(x)(I))(2). 

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References

SHOWING 1-10 OF 24 REFERENCES
Random fragmentation and coagulation processes
Fragmentation and coagulation are two natural phenomena that can be observed in many sciences and at a great variety of scales - from, for example, DNA fragmentation to formation of planets by
Ann
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
Phys
  • 54, 083301
  • 2013
Probability theory and mathematical statistics
Commun
  • Math. Phys. 50, 79
  • 1976
Phys
  • 18, 335
  • 1978
Israel J
  • Math. 147, 221
  • 2005
in Probability and Phase Transitions
  • edited by G. Grimmett, NATO Advanced Studies Institute, Series C: Mathematical and Physical Sciences
  • 1994
A 15
  • 1982
Lett
  • Math. Phys. 28, 75
  • 1993
...
...