5 research outputs found
Topological mixing of random substitutions
We investigate topological mixing of compatible random substitutions. For primitive random substitutions on two letters whose second eigenvalue is greater than one in modulus, we identify a simple, computable criterion which is equivalent to topological mixing of the associated subshift. This generalises previous results on deterministic substitutions. In the case of recognisable, irreducible Pisot random substitutions, we show that the associated subshift is not topologically mixing. Without recognisability, we rely on more specialised methods for excluding mixing and we apply these methods to show that the random Fibonacci substitution subshift is not topologically mixing
Sturmian Ground States in Classical Lattice-Gas Models
We construct for the first time examples of non-frustrated, two-body,
infinite-range, one-dimensional classical lattice-gas models without periodic
ground-state configurations. Ground-state configurations of our models are
Sturmian sequences defined by irrational rotations on the circle. We present
minimal sets of forbidden patterns which define Sturmian sequences in a unique
way. Our interactions assign positive energies to forbidden patterns and are
equal to zero otherwise. We illustrate our construction by the well-known
example of the Fibonacci sequences.Comment: published online 2019 in Journal of Statistical Physic