The Nature of the Transition in $d=4$ U(1) Lattice Gauge Theory

Gupta, Rajan; Novotny, Mark A.; Cordery, Robert

doi:10.1016/0370-2693(86)90221-2

The Nature of the Transition in $d=4$ U(1) Lattice Gauge Theory

Jan, 1985

7 pages

Published in:

Phys.Lett.B 172 (1986) 86-92

Published: 1986

DOI:

10.1016/0370-2693(86)90221-2

Report number:

NUB-2654-REV,
NUB-2654

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Abstract: (Elsevier)

The phase transition for the d = 4 compact U(1) lattice gauge theory has been studied using the Monte Carlo renormalization-group method. A single relevant eigenvalue is observed on the Wilson axis. The MCRG estimate for the exponent v changes with the coupling β ; an extrapolation towards β ∞ c provides an estimate v ∼ 0.42 rather than ∼ 0.33 as obtained by finite-size scaling. It is confirmed that loops of monopole current are the mechanism driving the transition. It is shown that at the transition the largest loop of monopole current undergoes a discontinuity in size and begins to span the lattice. On the basis of these findings, it is conjectured that on the Wilson axis the discontinuity is a finite-size effect.

Note:

Revised version

LATTICE FIELD THEORY: CRITICAL PHENOMENA
GAUGE FIELD THEORY: U(1)
RENORMALIZATION GROUP
CURRENT: MONOPOLE
NUMERICAL CALCULATIONS: MONTE CARLO

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