Thermodynamic Bethe ansatz for boundary sine-Gordon model Original Research Article

(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)/β2=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.