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Prog. Theor. Phys. Vol. 77 No. 2 (1987) pp. 473-490
The Triviality of Scalar Field Theories from the Viewpoint of Statistical Mechanics
Kei-ichi Kondo
Department of Physics, Nagoya University, Nagoya 464
(Received July 4, 1986)
Abstract:
The triviality or non-triviality of the continuum limit of scalar field theories is studied based on the behavior of the dimensionless renormalized coupling constant. In d>4 dimensions, the triviality of the continuum theory constructed as the scaling limit of lattice scalar theories can be understood as the violation of the hyperscaling relations. From this point of view, we derive a number of critical exponent inequalities. As an immediate consequence of them, the renormalized 6-point coupling constant together with the 4-point one can be shown to vanish in d>4 dimensions.
URL :
http://ptp.ipap.jp/link?PTP/77/473/
DOI : 10.1143/PTP.77.473
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Citing Article(s) :
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Progress of Theoretical Physics Vol. 79 No. 5 (1988) pp. 1217-1248
:
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Inconsistency of the λΦ4 Field Theory in High-Dimensions Constructed from the Broken-Symmetry Phase
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Kei-ichi Kondo
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Progress of Theoretical Physics Supplement No.92 (1987) pp. 1-13
:
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Scalar Field Theory from Statistical Mechanics
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Takashi Hara, Tetsuya Hattori, Kei-ichi Kondo and Hal Tasaki
