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Fluid states of matter can locally exhibit characteristics of the onset ofcrystalline order. Traditionally this has been theoretically investigated usingmultipoint correlation functions. However new measurement techniques now allowmultiparticle configurations of cold atomic systems to be observed directly.This has led to a search for new techniques to characterize the configurationsthat are likely to be observed. One of these techniques is the configurationdensity (CD), which has been used to argue for the formation of "Paulicrystals" by non-interacting electrons in e.g. a harmonic trap. We show herethat such Pauli crystals do not exist, but that other other interesting spatialstructures can occur in the form of an "anti-Crystal", where the fermionspreferentially avoid a lattice of positions surrounding any given fermion.Further, we show that configuration densities must be treated with great careas naive application can lead to the identification of crystalline structureswhich are artifacts of the method and of no physical significance. We analyzethe failure of the CD and suggest methods that might be more suitable forcharacterizing multiparticle correlations which may signal the onset ofcrystalline order. In particular, we introduce neighbour counting statistics(NCS), which is the full counting statistics of the particle number in aneighborhood of a given particle. We test this on two dimensional systems withemerging triangular and square crystal structures.

An investigation of pre-crystalline order, ruling out Pauli crystals and introducing Pauli anti-crystals