A Hamiltonian Model of Liquefaction and Crystallization in Three Dimensions

A model of a classical gas on a three‐dimensional sphere is discussed. The sphere is partitioned into cells, each corresponding to a different particle. The potential of each particle in its own cell is zero and, outside the cell, of order ln n, n being the number of particles. The two‐body interaction between the particles is shown to provoke (in the thermodynamic limit) a gas–liquid phase transition and a liquid–solid transition at a lower temperature. Both transitions are accompanied by a discontinuous drop of entropy.