Avoiding letter patterns in ternary square-free words

We consider special patterns of lengths 5 and 6 in a ternary alphabet. We show that some of them are unavoidable in square-free words and prove avoidability of the other ones. Proving the main results, we use Fibonacci words as codes of ternary words in some natural coding system and show that they can be decoded to square- free words avoiding the required patterns. Furthermore, we estimate the minimal local (critical) exponents of square-free words with such avoidance properties. © 2016, Australian National University. All rights reserved

Peculiar behavior of the electrical resistivity of MnSi at the ferromagnetic phase transition

The electrical resistivity of a single crystal of MnSi was measured across its ferromagnetic phase transition line at ambient and high pressures. Sharp peaks of the temperature coefficient of resistivity characterize the transition line. Analysis of these data shows that at pressures to ~0.35 GPa these peaks have fine structure, revealing a shoulder at ~ 0.5 K above the peak. It is symptomatic that this structure disappears at pressures higher than ~0.35 GPa, which was identified earlier as a tricritical poin