1999/11/30 by L. Leuzzi, Luca Leuzzi, Giorgio Parisi +1
Computer Science · Materials Science · Physics and Astronomy · #Cellular Automata and Applications #Quasicrystal Structures and Properties #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/33/23/301
published as J PHYS A-MATH GEN 33, 4215-4225 (2000) · 14 pages, 22 figures
arxiv created 2000/03/28 · openalex publication_date 2000/06/02 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
A 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.