Phase uniqueness for the Mallows measure on permutations
For a positive number q, the Mallows measure on the symmetric group is the probability
measure on S n such that P n, q (π) is proportional to q-to-the-power-inv (π) where inv (π) …
measure on S n such that P n, q (π) is proportional to q-to-the-power-inv (π) where inv (π) …
The free energy in a class of quantum spin systems and interchange processes
We study a class of quantum spin systems in the mean-field setting of the complete graph.
For spin S= 1 2, the model is the Heisenberg ferromagnet, and for general spin S∈ 1 2 …
For spin S= 1 2, the model is the Heisenberg ferromagnet, and for general spin S∈ 1 2 …
A direct proof of dimerization in a family of SU(n)-invariant quantum spin chains
We study the family of spin-S quantum spin chains with a nearest neighbor interaction given
by the negative of the singlet projection operator. Using a random loop representation of the …
by the negative of the singlet projection operator. Using a random loop representation of 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 …
interaction. A random loop model is introduced and relation to quantum spin systems is …
Decay of transverse correlations in quantum Heisenberg models
We study a class of quantum spin systems that include the S= 1 2 Heisenberg and XY-
models and prove that two-point correlations exhibit exponential decay in the presence of a …
models and prove that two-point correlations exhibit exponential decay in the presence of a …
Representation-theoretic approaches to several problems in probability
K Ryan - 2021 - qmro.qmul.ac.uk
In this thesis we study certain random walks on the two-dimensional lattice, known as the
Manhattan and Lorentz Mirror models, and certain quantum spin systems which are …
Manhattan and Lorentz Mirror models, and certain quantum spin systems which are …
On a class of orthogonal-invariant quantum spin systems on the complete graph
K Ryan - International Mathematics Research Notices, 2023 - academic.oup.com
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 it is …
the most general model invariant under the complex orthogonal group. In spin it is …
Violation of Ferromagnetic Ordering of Energy Levels in Spin Rings by Weak Paramagnetism of the Singlet
D Heson, S Starr, J Thornton - arxiv preprint arxiv:2307.12773, 2023 - arxiv.org
For the quantum Heisenberg antiferromagnet with spins-$ j $ on a bipartite, balanced graph,
the Lieb-Mattis" Ordering of energy levels" theorem guarantees that the ground state is a …
the Lieb-Mattis" Ordering of energy levels" theorem guarantees that the ground state is a …
Entanglement Entropy Bound and Emptiness Formation Probabilty of the XXZ Spin Chain
O Ogunkoya - 2022 - search.proquest.com
The first part of this thesis covers some of the background materials that are pre-requisite to
doing research in many body particle problems. The definitions are given from a …
doing research in many body particle problems. The definitions are given from a …
Rough Bounds for Emptiness Formation Probability in the 2d Dimer model using Reflection Positivity
S Starr, S Williams - arxiv preprint arxiv:1810.08846, 2018 - arxiv.org
We summarize how to obtain rough bounds for one version of the emptiness formation
probability in the 2d dimer model. The methods we use are the same as have been …
probability in the 2d dimer model. The methods we use are the same as have been …