virtuell

Random energy models (REM) suggested by B. Derrida turned out to be instrumental in the rigorous progress on statistical physics of disordered systems. Building on their success and motivated by interference phenomena, quantum physics, the Lee-Yang theory of phase transitions, the conjectured links with the Riemann zeta function and random matrix theory, we study several complex-valued versions of the REM. Specifically, we focus on the REM, the so-called generalized REM and on the so-called branching Brownian motion energy model. These are energy-based models of disordered systems, where the energy function is a complex-valued Gaussian process on a tree. In the two latter models, the energy function has strong correlations, while in the REM, the energy function is white noise. This allows us to explore the universality classes of the models by varying the strength of correlations. In all models, we identify the phase diagram, the fluctuations and the distribution of the zeros of the random partition function. To this end, we prove a range of non-standard limit theorems for the sums of strongly correlated random variables. Time permitting, we will discuss an ongoing work on models with microscopic interactions. The talk is based on joint works with Zakhar Kabluchko and Lisa Hartung.

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Anton Klimovsky

Uni Duisburg-Essen