For the lowest dimensions, they take on the following forms.

In lower dimension, some of the field lines pass through the barrier material wherein the screening has no effect.

The data lie approximately on a manifold of much lower dimension than the input space.

Both methods are only suitable for problems of low dimension.

We see that the problem quickly becomes intractable, even for low dimensions.

Usually, a phase space does not have a low enough dimension (two or three) to be pictured.

Below the lower critical dimension there is no phase transition.

Below the lower critical dimension, there is no field theory corresponding to the model.

Using this approach he has argued that near a black hole, quantum fields could be described by a theory in a lower dimension.

Interestingly, this is possible in a small number of low dimensions.