Emergence of macroscopic phenomena in the non-linear hyperbolic supersymmetric sigma model

Description

The non-linear supersymmetric hyperbolic sigma model introduced by Zirnbauer in 1991 can be seen as a statistical mechanical model of spins taking values on a supersymmetric non-linear manifold. This model has deep connections to a class of stochastic processes with memory called vertex-reinforced jump processes. These connections were successfully used to prove a phase transition in dimension larger or equal than 3 for the vertex-reinforced jump process. Nevertheless many important questions still remain open.

A powerful but difficult tool to study statistical mechanics models is the renormalization group. Our plan is to modify this approach in such a way that it applies to the non-linear supersymmetric hyperbolic sigma model. We expect this to help understanding the behavior of the model near the phase transition. In a first step, we will consider a simplified problem on a hierarchical lattice, where the construction is expected to be more accessible.

We have been working intensively, together and separately, on the non-linear supersymmetric hyperbolic sigma model and the connected vertex-reinforced jump process. One of us has also publications on the renormalization group in a different context.

Preprints/Publications

No preprints from this project yet.

Members

  • member's portrait

    Prof. Dr. Margherita Disertori

    Rheinische Friedrich-Wilhelms-Universität Bonn
    Principal Investigator
  • member's portrait

    Prof. Dr. Franz Merkl

    Ludwig-Maximilians-Universität München
    Principal Investigator
  • member's portrait

    Prof. Dr. Silke Rolles

    Technische Universität München
    Principal Investigator

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