Thermodynamics of a Tiling Model

Abstract

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.

14 pages, 22 figures

References in corpus (4)

• Measuring equilibrium properties in aging systems
• Violation of the Fluctuation Dissipation Theorem in Finite Dimensional Spin Glasses
• Response Function of Coarsening Systems
• Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems

Cited by in corpus (14)

• Glassy dynamics of kinetically constrained models
• Order in glassy systems
• Aperiodic compression and reconstruction of real world material systems based on Wang tiles
• First Order Phase Transition in a Model of Quasicrystals
• Level-set based design of Wang tiles for modelling complex microstructures
• Modelling quasicrystals at positive temperature
• A finite-temperature liquid-quasicrystal transition in a lattice model
• Statistical mechanics of glass transition in lattice molecule models
• Entropic commensurate-incommensurate transition
• Topological phase transition in a discrete quasicrystal
• Ordered amorphous spin system
• Ultra-slow dynamics in a translationally invariant spin model for multiplication and factorization
• Characterisation of the Set of Ground States of Uniformly Chaotic Finite-Range Lattice Models
• Aperiodicity in equilibrium systems: Between order and disorder