Electronic Structure Reading Group: Renormalization Group and Phase Transitions

At times, surprisingly simple mathematical models such as the Ising model can predict properties of macroscopic systems to multiple digits of accuracy. This is despite of the fact that in reality, many of these material properties arise from a much more complex interplay at the electronic structure level. Moreover, it can even be observed that the behavior of many seemingly unrelated systems can be described quantitatively by the same models, a phenomenon often called universality.
Such behavior and much more can be understood using the renormalization group, more correctly the renormalization "semi"group. It is a powerful mathematical technique used in various subfields of theoretical physics: quantum field theory, statistical mechanics and condensed matter physics. The session will provide a short introduction into this vast field, using the theory of phase transitions as the primary example. Due to the diverse background (math, physics, chemistry, MSE, etc.) of the audience, we will start with a more thorough motivation of the underlying ideas and prerequisites, slowly moving towards a more mathematical treatment of the renormalization group.

References:
1. Humphrey J. Maris and Leo P. Kadanoff; Teaching the Renormalization Group
2. Roland Bauerschmidt, David C. Brydges, and Gordon Slade; Introduction to a renormalisation group method [rigorous]
3. M. Kardar; Statistical Physics of Fields [non-rigorous]

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The electronic structure reading group brings together researchers and students interested in mathematical aspects of electronic structure problems and adjacent topics, including:

• Density Functional Theory
• Many-body Schrödinger equation for electrons
• Born-Oppenheimer Molecular Dynamics
• Numerical analysis and error control