Abstract
The exact vanishing of all β functions of the Callan-Symanzik equation is proved in a two-dimensional model with Thirring and gradient couplings: ( ψγ μψ) 2 , ( ψγ 5 γ μψ)ϱ μπ and ( ψγ μψ)ϱ μσ , where ψ, π and σ are fermion, pseudoscalar and scalar massive fields, respectively. The anomalous dimensions of scalar and pseudoscalar fields are also shown to be zero. Then we demonstrate that in two-dimensional models including at most one fermion field, only these three couplings can give asymptotic scale invariance.
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