Lattice radial quantization: 3D Ising

Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known Lagrangians. As an example, we employ a lattice shaped as a cylinder with a 2D Icosahedral cross-section to discretize...

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Bibliographic Details
Published in:Physics letters. B 2013-04, Vol.721 (4-5), p.299-305
Main Authors: Brower, R.C., Fleming, G.T., Neuberger, H.
Format: Article
Language:English
Subjects:
Cylinders
Deviation
Integers
Ising model
Lattices
Mathematical models
Quantization
Three dimensional
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Summary:Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known Lagrangians. As an example, we employ a lattice shaped as a cylinder with a 2D Icosahedral cross-section to discretize dilatations in the 3D Ising model. Using the integer spacing of the anomalous dimensions of the first two descendants (l=1,2), we obtain an estimate for η=0.034(10). We also observed small deviations from integer spacing for the 3rd descendant, which suggests that a further improvement of our radial lattice action will be required to guarantee conformal symmetry at the Wilson–Fisher fixed point in the continuum limit.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2013.03.009