Thermodynamics of Two-Component Log-Gases with Alternating Charges
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We consider a one-dimensional gas of positive and negative unit charges interacting via a logarithmic potential, which is in thermal equilibrium at the (dimensionless) inverse temperature β. In a previous paper [Šamaj, L. in J. Stat. Phys. 105:173–191, 2001], the exact thermodynamics of the unrestricted log-gas of pointlike charges was obtained using an equivalence with a (1+1)-dimensional boundary sine-Gordon model. The present aim is to extend the exact study of the thermodynamics to the log-gas on a line with alternating ± charges. The formula for the ordered grand partition function is obtained by using the exact results of the Thermodynamic Bethe ansatz. The complete thermodynamics of the ordered log-gas with pointlike charges is checked by a small-β expansion and at the collapse point β c =1. The inclusion of a small hard core around particles permits us to go beyond the collapse point. The differences between the unconstrained and ordered versions of the log-gas are pointed out.
KeywordsTwo-component log-gas Charge ordering Exact thermodynamics Thermodynamic Bethe ansatz
I am grateful to Peter Forrester for directing my attention to works about equivalence between the grand partition functions of unconstrained and ordered log-gases. The support received from Grant VEGA No. 2/0049/12 is acknowledged.