Data collection on the situation of neutral fermions in two-dimensional harmonic potential has allowed physicists for the first time to see the crystals Pauli and to investigate their melting. This was reported in a Preprint posted on arxiv.org
Crystal structure of physics often arises when the repulsive interaction between the particles kompensiruet some drawing power. For example, for the Wigner crystal Coulomb repulsion of electrons in one-dimensional conductor exceeds their kinetic energy, and the electrons are localized. In the case of a Coulomb crystal of ions kompensiruet repulsion overall potential of electromagnetic traps.
However, there is also a completely different mechanism of formation of symmetric structures, the indistinguishability of identical particles. It is evident even in the absence of interactions between particles. The Pauli exclusion principle States that two fermions cannot be in the same quantum state simultaneously, so if you put a few of noninteracting fermions in a common potential, it will inevitably lead to the emergence of anticorrelation between the various positions of the particles. In other words, the fermions organize themselves and form in the potential well of crystal-like structure, which minimizes the probability of finding two particles at the same point. This interaction of identical particles is called the exchange interaction, and the resulting structure is called a crystal Pauli.