Hans Koch, Charles Radin
Modelling quasicrystals at positive temperature
(113K, plain TeX, with ps figures)
ABSTRACT. We consider a two-dimensional lattice model
of equilibrium statistical mechanics, using nearest neighbor
interactions based on the matching conditions for an aperiodic
set of 16 Wang tiles. This model has uncountably many ground state
configurations, all of which are nonperiodic.
The question addressed in this paper is
whether nonperiodicity persists at low but positive temperature.
We present arguments, mostly numerical, that this is indeed the case.
In particular, we define an appropriate order parameter,
prove that it is identically zero at high temperatures,
and show by Monte Carlo simulation that it is
nonzero at low temperatures.