Appears in collection : 2024 - T1 - WS1 - Quantum simulators

Full Counting Statistics (FCS) is a way to characterise non-local correlations in many body systems. We calculate the generating function of FCS of the particle number on amacroscopic interval in a system of free fermions and reveal the existence of 2+\epsilon order phase transition as a function of the rescaled counting parameter. We characterise the transition as a topological change of the dominant configuration (instanton) in the coarse grained hydrodynamical fields similar to Limit Shape transitions in fluctuating statistical phenomena.