3D Ising and other models from symplectic fermions
Abstract
We study a model of N component symplectic fermions in D spacetime dimensions. It has an infra-red stable fixed point in 2<D<4 dimensions referred to as Sp{2N}{D}. Based on the comparison of exponents, we conjecture that the critical exponents for the 3D Wilson-Fisher fixed point for an O(N) invariant N-component bosonic field can be computed in the Sp{-2N}{3} theory. The 3D Ising model corresponds to Sp{-2}{3}. The exponent beta agrees with known results to 1 part in 1000 and is within current error bars. The nu exponent agrees to 1% and we suggest this because we only went to 1-loop for this exponent.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2006
- DOI:
- 10.48550/arXiv.cond-mat/0610817
- arXiv:
- arXiv:cond-mat/0610817
- Bibcode:
- 2006cond.mat.10817L
- Keywords:
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- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Disordered Systems and Neural Networks;
- High Energy Physics - Theory
- E-Print:
- This paper has been withdrawn by the author since further work did not lend more support to the conjecture, rather to the contrary