Ziv Rotman | Searcharxiv

arXiv2010

A finite-temperature liquid-quasicrystal transition in a lattice model

We consider a tiling model of the two-dimensional square-lattice, where each site is tiled with one of the sixteen Wang tiles. The ground states of this model are all quasi-periodic. The systems undergoes a disorder to quasi-periodicity phase transition at finite temperature. Introducing a proper order-parameter, we study the system at criticality, and extract the critical exponents characterizing the transition. The exponents obtained are consistent with hyper-scaling.

cond-mat.stat-mech↗

arXiv2010

Direct measurements of the dynamical correlation length indicate its divergence at an athermal glass transition

The super-cooled $N3$ model exhibits an increasingly slow dynamics as density approaches the model's random closest packing density. Here, we present a direct measurement of the dynamical correlation function $G_4(r,t)$, showing the emergence of a growing length scale $ξ_4$ across which the dynamics is correlated. The correlation length measured, up to 120 lattice sites, power-law diverges as the density approaches $ρ_t$, the density at which the fluid phase of the model is predicted to terminate. It is shown that the four-point susceptibility, often used as an agent to estimate $ξ_4$, does not depend simply on the latter. Rather, it depends strongly on the short-range behavior of $G_4(r,t)$. Consequently, $χ_4$ peaks before $ξ_4$ reaches its maximal value. The two quantities should therefore be studied independently.

cond-mat.stat-mech↗