Defects and Frustration (9, 11, 13, 16)

Why Not Double Twist Everywhere?

Parallel Transport along Closed Loop Doesn't Meet!
Blue Phase Parallel Transport has Negative Curvature in Flat Space
Rijij = -6 q^2
On sphere of radius 1/q in four dimensions, the curvature vanishes! There is an ideal template for double-twist there:

n(x) = q(-x1, x0, x3, -x2)

The Blue Phase is like a carpet made of orange peel (figure copyright Pamela Davis Kivelson): the edges of the cuts are the defect lines.

This research was paid for by THE US GOVERNMENT by the NSF.

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Last modified: November 2, 1995

James P. Sethna,

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).