Thermodynamic Properties of the One-Dimensional Two-Component Log-Gas

We consider a one-dimensional continuum gas of pointlike positive and negative unit charges interacting via a logarithmic potential. The mapping onto a two-dimensional boundary sine-Gordon field theory with zero bulk mass provides the full thermodynamics (density-fugacity relationship, specific heat, etc.) of the log-gas in the whole stability range of inverse temperatures $\beta<1$. An exact formula for the excess chemical potential of a ``foreign'' particle of an arbitrary charge, put into the log-gas, is derived. The results are checked by a small-$\beta$ expansion and at the collapse $\beta=1$ point. The possibility to go beyond the collapse temperature is discussed.