https://doi.org/10.1007/s100510050604
A geometric generalization of field theory to manifolds of arbitrary dimension
1
Fachbereich Physik, Universität GH Essen, 45117 Essen,
Germany
2
Department of Physics, MIT, Cambridge,
Massachusetts 02139, USA
Received:
15
October
1998
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
