# 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).

## Figures from this paper

Supersolid magnetic phase in the two-dimensional Ising-like antiferromagnet with strong single-ion anisotropy
• Physics, Materials Science
• 2017
The Ising model with the frustrated exchange interaction for strongly anisotropic antiferromagnetic ultrathin film is investigated in the mean field approximation at low temperatures. It is shown
Long-range order for the spin-1 Heisenberg model with a small antiferromagnetic interaction
We look at the general SU(2) invariant spin-1 Heisenberg model. This family includes the well-known Heisenberg ferromagnet and antiferromagnet as well as the interesting nematic (biquadratic) and the
Heisenberg models and Schur--Weyl duality
• Mathematics
• 2022
We present a detailed analysis of certain quantum spin systems with inhomogeneous (non-random) mean-field interactions. Examples include, but are not limited to, the interchangeand spin singlet
Quantum spin systems, probabilistic representations and phase transitions
This thesis investigates properties of classical and quantum spin systems on lattices. These models have been widely studied due to their relevance to condensed matter physics. We identify the
Existence of Néel Order in the S=1 Bilinear-Biquadratic Heisenberg Model via Random Loops
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
Quantum Spins and Random Loops on the Complete Graph
• Physics
• 2018
We present a systematic analysis of quantum Heisenberg-, xy - and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which
On a class of orthogonal-invariant quantum spin systems on the complete graph
We study a two-parameter family of quantum spin systems on the complete graph, which is the most general model invariant under the complex orthogonal group. In spin S = 1 2 it is equivalent to the
Universal behaviour of 3D loop soup models
These notes describe several loop soup models and their {\it universal behaviour} in dimensions greater or equal to 3. These loop models represent certain classical or quantum statistical mechanical
A numerical study of the 3D random interchange and random loop models
• Mathematics
• 2015
We have studied numerically the random interchange model and related loop models on the three-dimensional cubic lattice. We have determined the transition time for the occurrence of long loops. The

## 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
• Psychology
• 2005
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
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