Thermodynamics of a Tiling Model

Details Thermodynamics of a Tiling Model Thermodynamics of a Tiling Model

1999-11-02

arxiv.org/abs/cond-mat/9911020v2

J PHYS A-MATH GEN 33, 4215-4225 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages, 22 figures

Scientific paper

10.1088/0305-4470/33/23/301

A particular, two-dimensional, tiling model, composed by the so called Wang tiles 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 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 aging properties. The fluctuation-dissipation theorem is violated.

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