Prog. Theor. Phys. Vol. 70 No. 5 (1983) pp. 1207-1225
Supersymmetry and Quenched Random Fields Revisited
Department of Engineering Mathematics, Utsunomiya University, Utsunomiya 321
*Department of Applied Physics, Dalhousie University, Halifax, Nova Scotia B3H 3J5
(Received July 1, 1983)
The problem of obtaining the random field averages of the Green functions of the scalar field theories in the presence of the random field is reformulated in terms of the superfield Feynman rule in the supermomentum space. The system is fully investigated from the viewpoint of supersymmetry, and the most general expression for the dimensional reduction is given under the super-rotation symmetry. It is pointed out that there is a case when the dimensional reduction by 2 occurs in the tree approximation even if the long range force for the spins and the long range correlation of the random field are incorporated in the system provided they satisfy some relation. Some discussion is given on two kinds of the quantities which both exhibit the dimensional reduction from the viewpoint of satistical physics.
DOI : 10.1143/PTP.70.1207
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