I'm relatively new to the theoretical side of physics. I have a question about topology, continuous symmetry breaking and phase transitions. Your help is much appreciated!

Ok so I have an infinite array of metallic nanoparticles with a two atom basis, which can equivalently be thought of as two equivalent but independent sub-lattices (think of graphene). Anyway, I start with a configuration such that the lattice is a honeycomb structure (with three nearest neighbours), I then deform the lattice by scaling the position vector of the second basis particle, which can be seen in the figure as 0.9, 0.858, 0.856 and 0.8 times the original second basis particle vector.

I have generated plots which show if the resulting dispersion of the plasmons is gapless (cream) or gapped (orange) for arbitrary dipole orientation (am modelling the LSPs as dipoles).

Ok now I am going to say a paragraph and I would like you to tell me if I'm talking rubbish or not...

"At some value between $\vec{d}_3 = 0.9 \vec{e}_3$ and $\vec{d}_3 = 0.858 \vec{e}_3$ there is a topological change which can be seen in the breaking of the continuity of gapless states around the points $(\frac{\pi}{2},\frac{5\pi}{12})$ and $(\frac{\pi}{2},\frac{8\pi}{12})$. There is another topological change that occurs at a value between $\vec{d}_3 = 0.858 \vec{e}_3$ and $\vec{d}_3 = 0.856 \vec{e}_3$ where initially there is a continuum of gapless states about the lines $\theta = 0$ and $\theta = \pi$, then subsequently a continuum of gapped states about the same lines. At these values of $\vec{d}_3$ where a continuous translational symmetry has been broken, it is reasonable to assume this is accompanied by some form of phase transition."

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closed as too localized by Manishearth Apr 30 '13 at 20:29

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Well I ended up using an argument such as this in my dissertation, so I'll find out soon enough if this made any sense once my supervisor's marked it! Will report back incase anybody is interested


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