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Benjamin Lees

I am Ben and I am originally from Lancashire, England.

I completed an MMath degree at Warwick between 2008 and 2012 and am currently a forth year MASDOC student interested in Statistical Mechanics. I am supervised by Daniel Ueltschi and Roman Kotecký.

Current research

You can find my current CV here and a full research statement here.

My research interests include phase transitions in quantum and classical spin systems, in particular the phase diagram of the general SU(2) invariant two-body interaction in Spin-1. The development and application of probabilistic (loop) representations of quantum spin systems including dilute systems or systems of itinerant particles. Connections between probabilistic representations and correlations in quantum spin systems. (non)Decay of correlations in classical and quantum spin systems. Systems of dilute or itinerant lattice spin models and their phases. Correlation inequalities for quantum spin systems.

Preprints and publications

Long-range order for the spin-1 Heisenberg model with a small antiferromagnetic interaction Journal of Mathematical Physics 55, 093303 (2014) arXiv:1406.1044

Existence of Néel order in the S=1 bilinear-biquadratic Heisenberg model via random loops (Commun. Math. Phys.) (2016) OI:10.1007/s00220-016-2656-1 arXiv:1507.04942

Correlation inequalities for the quantum XY model with C. Benassi, D. Ueltschi (submitted to J. Stat. Phys.) (2016) arXiv:1510.03215

Staggered long-range order for diluted quantum spin models with R. Kotecký (Submitted to
J. Stat. Phys.) (2016) (arXiv:1605.06279).

Talks given

Here are some of the talks I have given during my PhD

Warwick statistical mechanics seminar
Neel order in a spin-1 lattice model using a random loop representation
Many-Body Quantum Systems - Warwick
Nematic phase transitions in the spin-1 model
NSF/CBMS Conference Quantum Spin Systems - UAB
Phase diagram of the spin-1 SU(2) invariant model
Spatial models in statistical mechanics - TU Darmstadt
Long range order in quantum spin systems
Postgraduate seminar - Warwick
Probabilistic representations of quantum spin systems
Postgraduate seminar - Warwick
The classical Heisenberg and related models
MASDOC retreat - Haworth
The spin-1 SU(2) invariant model
MASDOC retreat - Briavels
Dilute spin systems

Teaching

I have supervised five first year groups during my time at Warwick. I have previously been TA for MA3H3 (Set Theory) and MA4A7 (Quantum Mechanics: Basic Principles and Probabilistic Methods).

Contact

I can usually be found in the maths department in either B0.24 or the common room and emailed at b.lees@warwick.ac.uk.