Non-spherical lattices

4.10 Non-spherical lattices

Alternative topologies for the underlying simplicial complex were considered by Bilke et al. [51 , 53 ]. They showed that for topologies $S1 × S3$ and $T 4$ , the free energy agrees to leading order with that of $S4$ . Neither the critical value $κc(κ ,N ) 4 2 4$ , nor the leading contributions to the action density $⟨N ⟩∕N 2 4$ are changed. However, the simulations become more involved, since the size of the minimal configurations is increased.