1. in Statistical Physics
Conformal Invariance
in Statistical Physics
Part 1: Conformal invariance in general and a first glance at conformal field theory

2. Uniform dilation of the Ising model
above Tc

3. Uniform dilation
at Tc

4. Conformal Transformations
are transformations of space into itself that preserve angles.
locally look like combinations of translations, rotations, and dilations, but in general have different translations, rotations, and dilations at each point in space.

5. z’ = z /(2 – z) Special Conformal Transformations (SCT’s):
are conformal over the entire space (plane).
map lines and circles into lines and circles.
z’ = z /(2 – z)

6. SCT above Tc

7. SCT at Tc

8. z’ = z2 General Conformal Transformations (in 2D only):
are locally conformal in some region(s), but do not have to be conformal, or even defined, on the entire plane.
z’ = z2

9. z2 above Tc

10. z2 at Tc