Thermodynamic Limit of the Pieces’ Model

We study the ground states of pieces’ model in Fermi-Dirac statistics thermodynamic limit. In other words, we consider minimizing configurations n interacting fermions an interval [0, L] divided into pieces by a Poisson point process, when $$ \frac{n}{L}\rightarrow \rho >0 as L \rightarrow \infty . notice that decomposition groups arises from hypothesis finite-range pairwise interaction. Under assumptions convexity and non-degeneracy subsystems, get almost complete factorization any state. This method applies at least for comprising one or two particles. It improves expansion limit state energy per particle up to error O(\rho ^{2-\delta }) , with 0<\delta <1 [see Klopp Veniaminov (in: Frontiers Analysis Probability, Springer, Cham, 2020)]. also provides approximate model.