We consider a one-dimensional gas of positive and negative unit chargesinteracting via a logarithmic potential, which is in thermal equilibrium at the(dimensionless) inverse temperature $\beta$. In a previous paper [Samaj, L.: J.Stat. Phys. 105, 173-191 (2001)], the exact thermodynamics of the unrestrictedlog-gas of pointlike charges was obtained using an equivalence with a(1+1)-dimensional boundary sine-Gordon model. The present aim is to extend theexact study of the thermodynamics to the log-gas on a line with alternating$\pm$ charges. The formula for the ordered grand partition function is obtainedby using the exact results of the Thermodynamic Bethe ansatz. The completethermodynamics of the ordered log-gas with pointlike charges is checked by asmall-$\beta$ expansion and at the collapse point $\beta_c=1$. The inclusion ofa small hard core around particles permits us to go beyond the collapse point.The differences between the unconstrained and ordered versions of the log-gasare pointed out.
展开▼
