Condensed Matter Theory

Abstract:

A fundamental result relevant to spin chains and two-dimensional disordered systems is that the sphere sigma model with instanton coupling θ = π has a nontrivial low-energy fixed point and a gapless spectrum. This result is extended to two series of sigma models with θ = π: the SU(N)/SO(N) sigma models flow to the SU(N)1 Wess-Zumino-Witten theory, while the O(2N)/O(N) × O(N) models flow to O(2N)1 (2N-free Majorana fermions). These models are integrable, and the exact quasiparticle spectra and S matrices are found. One interesting feature is that charges fractionalize when θ = π. I compute the energy in a background field, and verify that the perturbative expansions for θ = 0 and π are the same as they must be. I discuss the flows between the two sequences of models, and also argue that the analogous sigma models with Sp(2N) symmetry, the Sp(2N)/U(N) models, flow to Sp(2N)1.

Abstract:

The torque induced between bounding surfaces in nematic liquid crystals due to thermal fluctuations was reported. The existence of Casimir torque due to anisotropy in the shape of the objects immersed in the complex fluid depended on the relative orientation of these objects. The torques were calculated for a simple geometry in the absence of elastic effects. These calculations suggested a direct measure of the torque exerted between two plates at fixed separation and a measure of force as a function of separation for plates at various angles.