14 citations · 54 across the 14 of their papers we have counts for
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Phase transition for loop representations of Quantum spin systems on trees
Volker Betz, Johannes Ehlert, Benjamin Lees
We consider a model of random loops on Galton-Watson trees with an offspring distribution with high expectation. We give the configurations a weighting of . For…
Correlation inequalities for classical and quantum XY models
Costanza Benassi, Benjamin Lees, Daniel Ueltschi
We review correlation inequalities of truncated functions for the classical and quantum XY models. A consequence is that the critical temperature of the XY model is necessarily sma…
Correlation inequalities for the quantum XY model
Costanza Benassi, Benjamin Lees, Daniel Ueltschi
We show the positivity or negativity of truncated correlation functions in the quantum XY model with spin 1/2 (at any temperature) and spin 1 (in the ground state). These Griffiths…
Existence of Néel order in the S=1 bilinear-biquadratic Heisenberg model via random loops
Benjamin Lees
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. Usin…
Long-range order for the spin-1 Heisenberg model with a small antiferromagnetic interaction
Benjamin Lees
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 (b…