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

Abstract

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 2 ℓ 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 ) , β ] , at inverse temperature β , has an infinite number of singularities, as a function of ℓ / a .