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

Uniform dilation of the Ising model above Tc

Uniform dilation at Tc

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.

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)

SCT above Tc

SCT at Tc

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

z2 above Tc

z2 at Tc