Luca Leuzzi and Giorgio Parisi 2000 J. Phys. A: Math. Gen. 33 4215 doi:10.1088/0305-4470/33/23/301
Luca Leuzzi1 and Giorgio Parisi2
Show affiliationsA specific two-dimensional tiling model, composed of the so-called Wang tiles has been studied at finite temperature using Monte Carlo numerical simulations. In the absence of any thermal bath the Wang tiles provide the opportunity of building a very large number of non-periodic tilings. We can construct a local Hamiltonian such that only perfectly matched tilings are ground states with zero energy. This Hamiltonian has a very large degeneracy. The thermodynamic behaviour of such a system seems to show a continuous phase transition at non-zero temperature. An order parameter with non-trivial features is proposed. Under the critical temperature the model exhibits ageing properties. The fluctuation-dissipation theorem is violated.
82B30 Statistical thermodynamics (See also 80-XX)
82B26 Phase transitions (general)
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
Issue 23 (16 June 2000)
Received 8 November 1999, in final form 31 March 2000
Luca Leuzzi and Giorgio Parisi 2000 J. Phys. A: Math. Gen. 33 4215
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