Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modelling gravity on a hyper-cubic lattice   We present an elegant and simple dynamical model of symmetric, non-degenerate
(n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic
lattice with nearest-neighbor interactions. We show how this model is related
to General Relativity, and discuss multiple ways in which it can be useful for
studying gravity, both classical and quantum. In particular, we show that the
dynamics of the model when all matrices are close to the identity corresponds
exactly to a finite-difference discretization of weak-field gravity in harmonic
gauge. We also show that the action which defines the full dynamics of the
model corresponds to the Einstein-Hilbert action to leading order in the
lattice spacing, and use this observation to define a lattice analogue of the
Ricci scalar and Einstein tensor. Finally, we perform a mean-field analysis of
the statistical mechanics of this model.

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an