  A numerical investigation of a non-commutative field theory defined via the
spectral action principle is conducted. The construction of this triple relies
on an 8-dimensional Clifford algebra. Following to the standard procedure of
non-commutative geometry, the spectral action is computed for the product of
the triple (A,H,D) with a matrix-valued spectral triple. Using Monte Carlo
simulation we study various quantities such as the energy density, the specific
heat density and some order parameters varying the matrix size and the
independent parameters of the model.
