14 citations · 54 across the 14 of their papers we have counts for
17 papers
Infinite-mean Galton-Watson trees have zero random-interchange threshold
Andreas Klippel, Benjamin Lees, Christian Mönch
We prove that, on a Galton-Watson tree with almost surely finite offspring and infinite offspring mean, the random interchange process has critical parameter zero for infinite cycl…
Rainbow percolation
Peter Gracar, Benjamin Lees
We consider the weight-dependent random connection model on a Poisson point process of intensity on in which the vertices and are joined…
Loop vs. Bernoulli percolation on trees: strict inequality of critical values
Andreas Klippel, Benjamin Lees, Christian Mönch
We study loop ensembles on locally finite rooted trees. The loops are induced by a Poisson process of links on the edges; the transposition-only case is the random interchange proc…
Combinatorial identities from an inhomogeneous Ising chain
Jessica Jay, Benjamin Lees
We study a family of inhomogeneous Ising chain models along with an equivalent family of nearest neighbour particle systems. By the correspondence between the two families we prove…
Griffiths inequalities for the -spin model
Benjamin Lees
We prove Griffiths inequalities for the -spin model with inhomogeneous coupling constants and external magnetic field for any . This is achieved by using a represent…
Correlation inequalities for the uniform 8-vertex model and the toric code model
Jakob E. Björnberg, Benjamin Lees
We elucidate connections between four models in statistical physics and probability theory: (1) the toric code model of Kitaev, (2) the uniform eight-vertex model, (3) random walk…
Exponential decay of transverse correlations for O(N) spin systems and related models
Benjamin Lees, Lorenzo Taggi
We prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary (non-zero) values of the external magnetic field and arbitrary spin dimension N > 1. Our…
Site-monotonicity properties for reflection positive measures with applications to quantum spin systems
Benjamin Lees, Lorenzo Taggi
We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity p…
Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N
Benjamin Lees, Lorenzo Taggi
We provide a uniformly-positive point-wise lower bound for the two-point function of the classical spin model on the torus of , , when $N \in \mathbb…
Sharp phase transition for random loop models on trees
Volker Betz, Johannes Ehlert, Benjamin Lees +1
We investigate the random loop model on the -ary tree. For , we establish a (locally) sharp phase transition for the existence of infinite loops. Moreover, we derive r…
The interchange process with reversals on the complete graph
Jakob E. Björnberg, Michał Kotowski, Benjamin Lees +1
We consider an extension of the interchange process on the complete graph, in which a fraction of the transpositions are replaced by `reversals'. The model is motivated by statisti…
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…
Staggered long-range order for diluted quantum spin models
Roman Kotecký, Benjamin Lees
We study an annealed site diluted quantum XY model with spin . We find regions of the parameter space where, in spite of being a priori favourable for a…
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…