Warwick Statistical Mechanics Seminar
in the Department of Mathematics
 |
This term, all seminars take place Thursdays at 2pm, room MS.04 (Zeeman Building), unless indicated otherwise. |
 Raphaël Lefevere, 13.06.2013 |
| 09.10.2025 | |
| 16.10.2025 | Kieran Ryan (University of Vienna) Ground states in the XXZ chain and the Lorentz mirror model with loop weight 2 We present some work in progress on infinite volume ground states of a quantum spin system in 1 dimension known as the Heisenberg XXZ chain. The work uses a representation of the chain as a probabilistic continuous time model of loops due to Ueltschi. The Lorentz mirror model with loop weight 2 is a model of random loops on Z^2. It can be thought of as a discrete time version of the quantum loop model, and has a simple coupling with the 6-vertex model. We use a recent result of Glazman and Lammers on the six-vertex model and a further, new coupling to show that for the Lorentz loop model, certain finite volume measures converge to a common infinite volume measure, which exhibits no infinitely long loops, and has slow decay of connection probabilities. Work is in progress on the same statement in the quantum loop model, and its consequences for the XXZ model: certain finite volume, finite temperature states converge to a common infinite volume ground state, with slowly decaying spin-spin correlations. In particular, these arguments do not use any integrability or exact solutions - just percolation-type arguments. We will introduce the several models involved here slowly and give some ideas of how they relate to one another. Contact: Daniel |
| 23.10.2025 | |
| 30.10.2025 | |
| 06.11.2025 | |
| 13.11.2025 | |
| 20.11.2025 | |
| 27.11.2025 | |
| 04.12.2025 | |
| 11.12.2025 | |