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Critical points in less than two dimensions

From a study of the liquid-vapour equilibrium at low temperatures in the lattice-gas and penetrable-sphere models it is concluded that the phase transformation can occur as soon as the dimensionality of the fluid exceeds one, even if, formally, by a small, non-integral amount. A hypothetical fluid of dimensionality s only slightly greater than 1 is defined through its cluster integrals, and its thermodynamic properties are deduced. It is found that its behaviour is identical to that of a one-dimensional system for temperatures above some critical temperature T c (with T c →0 as s →1), while for temperatures below T c its behaviour is that of a two-phase system of dimensionality s greater than 1.