Nevertheless, they exhibit a non-trivial ultraviolet fixed point of the renormalization group both in the lattice formulation[3][4] and in the double expansion originally proposed by Kenneth G.
In addition, the improved lattice or quantum field theory predictions can then be compared to laboratory experiments on critical phenomena, since the O(n) model describes physical Heisenberg ferromagnets and related systems.
The above results point therefore to a failure of naive perturbation theory in describing correctly the physical behavior of the O(n)-symmetric model above two dimensions, and to the need for more sophisticated non-perturbative methods such as the lattice formulation.
When computing path integrals, the functional measure needs to be "weighted" by the square root of the determinant of g, This model proved to be relevant in string theory where the two-dimensional manifold is named worldsheet.
Further adding nonlinear interactions representing flavor-chiral anomalies results in the Wess–Zumino–Witten model,[7] which augments the geometry of the flow to include torsion, preserving renormalizability and leading to an infrared fixed point as well, on account of teleparallelism ("geometrostasis").