Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Study of potential Hamiltonians for quantum graphity   In this work we show that the simple Hamiltonians used in Quantum Graphity
models are highly degenerate, having multiple ground states that are not
lattices. In order to assess the distance of the resulting graphs from a
lattice graph, we propose a new measure of the equivalence of vertices in the
graph. We then propose a Hamiltonian that has a rectangular lattice as a ground
state that appears to be non-degenerate. The resulting graphs are close to
being a rectangular lattice, and the defects from the perfect lattice seem to
behave like particles of quantized mass that attract one another.

2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs