A particular, two-dimensional, tiling model, composed by the so-called Wang tiles [1] has been studied at finite temperature by Monte Carlo numerical simulations. In absence of any thermal bath the Wang tiles give the opportunity of building a very large number of aperiodic tiling. Considering these as ground states and assigning to the perfectly matched tiling the ground state energy value, the system shows a very high degeneracy. Its thermodynamic behaviour shows a second order phase transition at non zero temperature. Under the critical temperature the model exhibits aging properties. The fluctuation-dissipation theorem is violated and the relation between the correlation and the response function is very similar to that found in other models representing glassy systems. Also the spatial correlations between tiles and their behaviour varying the temperature have been analyzed.

1. B. Gruenbaum, G.C. Shephard. Tilings and patterns - New York: W.H. Freeman , (1987)

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