Multiple Singularities of the Equilibrium Free Energy in a One-Dimensional Model of Soft Rods.

There is a misconception, widely shared among physicists, that the equilibrium free energy of a one-dimensional classical model with strictly finite-ranged interactions, and at nonzero temperatures, cannot show any singularities as a function of the coupling constants. In this Letter, we discuss an instructive counterexample. We consider thin rigid linear rods of equal length 2l whose centers lie on a one-dimensional lattice, of lattice spacing a. The interaction between rods is a soft-core interaction, having a finite energy U per overlap of rods. We show that the equilibrium free energy per rod F[l/a), beta], at inverse temperature beta, has an infinite number of singularities, as a function of l/a.