caa a22 4500 463195515 CHVBK 20180406164921.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s10773-006-9300-3 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9300-3 Critical Exponents from the Resummed Effective Potential of the $$({\frac{g}{4}}\phi^{4}-J\phi)_{1+1}$$ Scalar Field Theory [Elektronische Daten] [Abouzeid. Shalaby, S. El-Basyouny] 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 g 3. 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 g 3 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. Springer Science+Business Media, LLC, 2007 effective potential nationallicence critical phenomena nationallicence exponents nationallicence Borel resummation nationallicence Shalaby Abouzeid Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, P.O. Box 35516, Mansoura, Egypt aut El-Basyouny S. Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, P.O. Box 35516, Mansoura, Egypt aut International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/6(2007-06-01), 1617-1635 0020-7748 46:6<1617 2007 46 10773 https://doi.org/10.1007/s10773-006-9300-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9300-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shalaby Abouzeid Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, P.O. Box 35516, Mansoura, Egypt aut NATIONALLICENCE 700 1- El-Basyouny S. Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, P.O. Box 35516, Mansoura, Egypt aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/6(2007-06-01), 1617-1635 0020-7748 46:6<1617 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer