18.2. Analytic structure of the S-matrix of the Bullogh–Dodd model

a. Study the structure of the poles and zeros of the S-matrix of the Bullogh–Dodd model S(θ) = f23

(θ) f−B3

(θ) f B−2 3

(θ)

with B(λ) = λ2 2π
1 1+ λ2 4π
by varying the coupling constant λ.

b. Make the analytic continuation B→1+ 3 iπ
β0 with β0 real and show that in the limit β0→∞the S-matrix of the Bullogh–Dodd model reduces to the S-matrix of the Yang–Lee model.