#### Condensed Matter Seminar - Adam Nahum, University of Oxford "Loop models, vortex lines, and SU(n) magnets"

Abstract: I will discuss two apparently disparate types of critical phenomenon which are tied together by the language of loop models. The first arises at geometrical phase transitions in disordered 3D systems with vortex line defects. These defects can undergo percolation-like transitions at which the typical size of a vortex loop diverges, and we might ask: what field theory describes the universal fractal geometry of the loops at such a transition? Using a mapping to a lattice gauge theory, I will argue that the answer is the CP^{n-1} sigma model in the replica limit n-->1. This field theory (for n=2,3...) is more familiar in the context of transitions between Neel and dimerized phases in 2D quantum magnets with SU(n) symmetry. I will argue that a class of 3D classical loop models provides a unified description of the critical behaviour in all of these problems, and a useful tool for Monte Carlo analysis of (confined and deconfined) critical points in SU(n) magnets. I will briefly present numerical results for SU(2) and SU(3) magnets.

**Location:**
PCTS Seminar Room

**Date/Time: **09/24/12
at
1:15 pm
- 09/24/12
at
2:30 pm

**Category: **Condensed Matter Seminar

**Department: **Physics