Irreversible growth of binary mixtures on small-world networks

TL;DR

This paper investigates how binary mixtures grow on small-world networks, revealing that even a small fraction of shortcuts induces a continuous phase transition, unlike in regular lattices, with critical behavior analyzed via Monte Carlo simulations.

Contribution

It demonstrates that small-world network topology induces criticality in non-equilibrium binary mixture growth, providing phase diagrams and critical exponents through extensive simulations.

Findings

Phase transition occurs for any p>0

Critical exponents are evaluated

Small-world networks trigger criticality similar to equilibrium systems

Abstract

Binary mixtures growing on small-world networks under far-from-equilibrium conditions are studied by means of extensive Monte Carlo simulations. For any positive value of the shortcut fraction of the network ($p>0$), the system undergoes a continuous order-disorder phase transition, while it is noncritical in the regular lattice limit ($p=0$). Using finite-size scaling relations, the phase diagram is obtained in the thermodynamic limit and the critical exponents are evaluated. The small-world networks are thus shown to trigger criticality, a remarkable phenomenon which is analogous to similar observations reported recently in the investigation of equilibrium systems.