DIMENSIONAL DEPENDENCE OF CHIRAL-SYMMETRY- BREAKING PHASE TRANSITION IN QUENCHED PLANAR QED

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Abstract
We consider the critical behavior of the phase transition associated with the spontaneous breaking of chiral-symmetry in (QED) D, in the framework of the Schwinger-Dyson equation. Special attention is paid on the scaling law. While it is well known that quenched planar QED 4 obeys the Miransky scaling of the essential singularity type, our numerical calculations show that QED 5 and QED 6 do obey the mean-field type scaling, even in the quenched planar approximation. Thus the essential singularity type scaling in the cutoff QED is considered to be possible only when D=4 under the quenched planar approximation.

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