The Migdal Recursion Equation as a Probe for Crossover Points : Lattice Gauge Theory on Discrete Groups

概要

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Four dimensional lattice gauge theories (LGT ) on discrete groups, Z(N) and the subgroups of SU(2), Q, T^^~, O^^~ and I^^~, are investigated on the basis of the Migdal approximation. In the recursion equation, the partition function is given in somewhat general way by the irreducible characters. For Z(2), Z(3) and Z(4) LGT the critical point β_c is exactly in agreement with the value estimated from the self duality. For Z(N) (N≥5) LGT, β_c is nearly 1 and almost independent of N. As for the subgroups of SU(2), β_c is near a first order critical point of Monte Carlo simulations for Q and T^^~ and β_c is mear the crossover point (β≃2) for O^^~ and I^^~. The application of a similar parametrization of the partition function to continuous groups, U(1) and SU(2), results in β_c≃0.92 and 1.9, respectively. The latter value is very close to the crossover point (β≃2) in Creutz's result. The relation between our results and the roughening transition is discussed.
理論物理学刊行会の論文
1981-09-25