Elsevier

Nuclear Physics B

Volume 230, Issue 3, 26 March 1984, Pages 385-406
Nuclear Physics B

Perturbative corrections to Migdal-Kadanoff recursion relations for Z4 theory

https://doi.org/10.1016/0550-3213(84)90219-0Get rights and content

Abstract

For the Z4 lattice gauge theory in four dimensions or the associated spin system in two dimensions we examine the critical structure by making a correction to the bond-shifting operator. This is done for the most general single plaquette or nearest neighbor action. The two-dimensional problem in coupling space becomes a four-dimensional problem when the correction is made to the bond-shifting operators. The four-dimensional problem is decomposed into two two-dimensional problems which allows for the effective application of the Migdal-Kadanoff recursion relations in differential form. The solutions to the two-dimensional problems are then recomposed into the solution of the original two-dimensional problem in coupling space. Of particular interest is the region β2 < 0, β1 ⩾ 0, where β1 and β2 are the coupling constants in the fundamental and adjoint representations respectively. We find a critical structure, including a second crossover, which leads to a splitting of the phase structure in this region which is in agreement with Monte Carlo predictions.

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Cited by (6)

This work was supported by the US Department of Energy under contract number DE-AC02-76CH00016.

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