Statistical-Mechanical Theory of One-Dimensional Gases with Short-Range and Long-Range Intermolecular Forces. II. Phase Transitions at the Absolute Zero

Abstract

The model of one-dimensional gas (proposed in the preceding paper I) of molecules with hard cores, with short-range interactions given by a nearest-neighbour (repulsive or attractive) square potential and with infinitely-long-range interactions given by the attractive potential −2a⁄L (a=positive constant, L=length of the gas, L→∞ with length per molecule fixed) is rigorously treated at the absolute zero; especially its phase transitions are investigated. It is deduced that, at the absolute zero, this model in the case of repulsive short-range interaction exhibits two transitions (the gas-liquid and the liquid-solid transition) if the long-range attraction is weak enough, and exhibits only one transition (the gas-solid transition) if the long-range attraction is strong enough, and this model in the case of attractive short-range interaction exhibits only one transition (the gas-solid transition).