On the renormalized coupling constant and the susceptibility in φ44 field theory and the Ising model in four dimensions
作者： Michael Aizenman , Ross Graham
DOI: 10.1016/0550-3213(83)90053-6
关键词: Mathematical physics 、 Physics 、 Coupling constant 、 Magnetic susceptibility 、 Quantum mechanics 、 Euclidean geometry 、 Mean field theory 、 Field theory (psychology) 、 Limit (mathematics) 、 Ising model 、 Quantum field theory
摘要: Abstract We discuss the euclidean φ 4 field theory, and critical behavior in ferromagnetic systems four dimensions. It is rigorously shown that there are at most logarithmic corrections to mean law of magnetic susceptibility X = ΣS 2 (0, x ). Furthermore, if any such present a continuum limit which used construct limiting theory would be non-interacting. Our analysis extends variables belong Griffiths-Simon class.
harvard.edu
princeton.edu
elsevier.com
sci-hub.se 参考文章(14)
Oliver A. McBryan, Jay Rosen, Existence of the critical point in φ4 field theory Communications in Mathematical Physics. ,vol. 51, pp. 97- 105 ,(1976) , 10.1007/BF01609341
Kenneth G. Wilson, Michael E. Fisher, Critical Exponents in 3.99 Dimensions Physical Review Letters. ,vol. 28, pp. 240- 243 ,(1972) , 10.1103/PHYSREVLETT.28.240
Alan D. Sokal, A rigorous inequality for the specific heat of an Ising or φ4 ferromagnet Physics Letters A. ,vol. 71, pp. 451- 453 ,(1979) , 10.1016/0375-9601(79)90633-9
Charles M. Newman, Inequalities for Ising models and field theories which obey the Lee-Yang Theorem Communications in Mathematical Physics. ,vol. 41, pp. 1- 9 ,(1975) , 10.1007/BF01608542
Barry Simon, Correlation inequalities and the decay of correlations in ferromagnets Communications in Mathematical Physics. ,vol. 77, pp. 111- 126 ,(1980) , 10.1007/BF01982711
Joel L. Lebowitz, GHS and other inequalities Communications in Mathematical Physics. ,vol. 35, pp. 87- 92 ,(1974) , 10.1007/BF01646608
Robert B. Griffiths, C. A. Hurst, S. Sherman, Concavity of Magnetization of an Ising Ferromagnet in a Positive External Field Journal of Mathematical Physics. ,vol. 11, pp. 790- 795 ,(1970) , 10.1063/1.1665211
J. Fröhlich, B. Simon, T. Spencer, Infrared Bounds, Phase Transitions and Continuous Symmetry Breaking Communications in Mathematical Physics. ,vol. 50, pp. 79- 95 ,(1976) , 10.1007/BF01608557
Michael Aizenman, Proof of the Triviality of ϕ d 4 Field Theory and Some Mean-Field Features of Ising Models for d > 4 Physical Review Letters. ,vol. 47, pp. 1- 4 ,(1981) , 10.1103/PHYSREVLETT.47.1
Barry Simon, Robert B. Griffiths, The (φ4)2 Field Theory as a Classical Ising Model Communications in Mathematical Physics. ,vol. 33, pp. 145- 164 ,(1973) , 10.1007/BF01645626