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Conformal Invariance 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 T c. Uniform dilation at T c. Conformal Transformations.

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Conformal Invariance in Statistical Physics

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  1. 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. 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. 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

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