A geometric generalization of field theory to manifolds of arbitrary dimension
Fachbereich Physik, Universität GH Essen, 45117 Essen,
2 Department of Physics, MIT, Cambridge, Massachusetts 02139, USA
Accepted: 4 November 1998
Published online: 15 January 1999
We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for , while leads to self-avoiding tethered membranes (as the O(N) model reduces to self-avoiding polymers). The model is studied perturbatively by a 1-loop renormalization group analysis, and exactly as . Freedom to choose the expansion point D, leads to precise estimates of critical exponents of the O(N) model. Insights gained from this generalization include a conjecture on the nature of droplets dominating the 3d-Ising model at criticality; and the fixed point governing the random bond Ising model.
PACS: 05.70.Jk – Critical point phenomena / 11.10.Gh – Renormalization / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 75.10.Hk – Classical spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999