Upper critical dimension

Summary

The upper critical dimension of a family of models is the dimension above which their critical behaviour is described exactly by mean-field theory. Above it, fluctuations are too weak to change the critical exponents. At the upper critical dimension itself, mean-field exponents hold up to logarithmic corrections. It is $4$ for the Ising and $O(n)$ models with short-range interactions and $6$ for percolation.