**ANGELO LUCIA**University of Copenhagen

The standard approach to mathematically describe phase transitions in classical and quantum many-body models is to consider sequences of increasing size and then study their limit, which is usually called the "thermodynamic limit". Of course numerical simulations and real world experiments can only consist of a finite number of particles, from which is sometimes possible to extrapolate information about what happens in the limit.

While this approach has been generally very successful, it was shown recently that properties of the thermodynamic limit can be undecidable, i.e. there cannot exist an algorithm which decides whether they are present or not. This implies that very exotic behavior can appear: as an example, we show how to construct quantum lattice models which appears to be classical at finite sizes but will reveal their nature of a topological models at system sizes inaccessible for all practical purposes.
**Seminar, March 22, 2017, 12:00. Seminar Room
Hosted by Prof. Antonio Acín **