Crystallization conjecture for classical many-particle systems

Determine whether the ground states of classical many-particle systems are usually crystalline, as asserted by the crystallization conjecture.

Background

The paper opens by contrasting the usual expectation of crystalline ordering in zero-temperature classical many-particle systems with examples of systems whose ground states remain disordered. The crystallization conjecture is presented as the general principle that ground states are typically crystalline, in accordance with the third law of thermodynamics.

The one-dimensional fluids studied in the paper provide explicitly solvable exceptions for concave finite-range nearest-neighbour potentials: at a special incompressibility pressure, their ground states are disordered and non-hyperuniform. Thus, these models motivate examining the scope and validity of the broad crystallization claim.