Critical Exponents from the Resummed Effective Potential of the $$({\frac{g}{4}}\phi^{4}-J\phi)_{1+1}$$ Scalar Field Theory

Abstract

We establish a unified way for the calculation of the critical exponents, without the use of epsilon expansion, through the improvement of the perturbative effective potential of the 1+1 dimensional \(({\frac{g}{4}}\phi^{4}-J\phi)\) scalar field theory. First, we obtain the perturbation series for the effective potential up to g3. We improved the perturbative effective potential by establishing a parameter-free resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g3 order, we found a complete agreement between our resummed effective potential and the well known features from constructive field theory. We prove that the 1-PI correlation functions and the effective potential ought to have the same large order as well as strong coupling behaviors. We computed the critical exponents and our results show a good agreement with the exact Ising model values.