Magnetism is an active area of research and frustrated magnets are especially intriguing. Frustration means that it is impossible to satisfy energetically all the magnetic interactions in the material simultaneously.
About ten years ago we invented a diagrammatical/numerical method, the Nematic Bond Theory, for calculating properties of classical frustrated magnets (M. Schecter, O.F. Syljuasen, and J. Paaske, "Nematic Bond Theory of Heisenberg Helimagnets", Phys. Rev. Lett. 119, 157202, (2017).). This framework uses diagrammatic techniques from statistical field theory to arrive at a set of self-consistent equations which are then solved numerically to give information about phases, phase transitions, free energies and critical temperatures. It has already been used for many magnetic systems with considerable success. However, the method has one major approximation; vertex corrections are ignored.
This goal of this project, which is very challenging, is to quantify the error due to the neglected vertex corrections.
The type of work in this project will be mostly analytical; involving the use of Feynman diagrams and field-theory techniques, but also numerical in quantifying the errors.