The low-temperature properties of the one-dimensional fluid

Abstract

The low-temperature properties of a one-dimensional fluid with hard core attractive nearest-neighbor interactions have been investigated. The fluid exhibits a critical behavior nearT=0 which is, in some respects, analogous to that of the one-dimensional Ising models. With the proper choice of scaling variables the singular part of the appropriate thermodynamic potential has the same homogeneous scaling form as the Ising model. The correlations in the scaling region have a more complex structure than in the Ising model but do have a long-ranged part of scaling form. TheT=0 limit in the scaling region gives states of low density and zero pressure whose correlations are those of a two-phase state, of which one component is a perfect crystal phase and the other is a zero density phase. The positive pressureT=0 states are single-phase perfect crystal states whose long-range order develops continuously asT approaches zero. Those Fourier components of the correlations, which correspond to reciprocal lattice vectors, diverge asT approaches zero; hence, the transition is second-order, unlike higher-dimensional systems.