Spin foam models are particular models aimed at finding a theory of quantum gravity. Their relation to Einstein-Hilbert gravity in classical limit seems however not to be convincingly argued for in the literature.
Winston J. Fairbairn, Etera R. Livine, 3D spinfoam quantum gravity: matter as a phase of the group field theory-, Classical Quantum Gravity 24 (2007), no. 20, 5277–5297 MR2351342,doi
D. V. Boulatov, A model of three-dimensional lattice gravity, Modern Phys. Lett. A 7 (1992), no. 18, 1629–1646, MR94c:83039, doi
A. Perez, Spin foam models for quantum gravity, Class. Quant. Grav. 20 (2003) R43, arXiv:gr-qc/0301113
Sergei Alexandrov, Philippe Roche, Critical overview of loops and foams, arxiv/1009.4475
Winston Fairbairn, Etera R. Livine, 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory, Class.Quant.Grav. 24:5277-5297, 2007, arxiv/gr-qc/0702125, doi
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