Thermodynamic Bethe Ansatz for boundary sine-Gordon model

(R-channel) TBA is elaborated to find the effective central charge dependence on the boundary parameters for the massless boundary sine-Gordon model with the coupling constant $(8π) /β^2 = 1+ λ$ with $λ$ a positive integer. Numerical analysis of the massless boundary TBA demonstrates that at an appropriate boundary parameter range (cusp point) there exists a singularity crossing phenomena and this effect should be included in TBA to have the right behavior of the effective central charge.

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