Interplay between thermal percolation and jamming upon dimer adsorption on binary alloys

TL;DR

This study uses Monte Carlo simulations to explore how the structural order of binary alloy substrates, affected by temperature, influences the jamming and percolation of dimers, revealing a complex interplay near the phase transition.

Contribution

It introduces a temperature-dependent model linking alloy order-disorder transition to dimer jamming and percolation, highlighting a new phase diagram and universality class preservation.

Findings

Jamming prevents percolation below a critical temperature T*

Percolation occurs above T* with standard universality class

Fractal dimension of percolating clusters remains consistent across temperatures

Abstract

Using Monte Carlo simulations we study jamming and percolation processes upon the random sequential adsorption of dimers on binary alloys with different degrees of structural order. We obtain the equimolar mixtures used as substrates by applying the isomorphism between an alloy and the Ising model (conserved order parameter). The annealing temperature $T$ of the mixture then is a continuous parameter that characterizes the different sets of substrates, shaping the deposition process. As the alloy undergoes an order-disorder phase transition at the Onsager critical temperature ($T_{c}$), the jamming and percolating properties of the dimers deposited over the substrate are subjected to non-trivial changes. These are reflected in a density-temperature phase diagram with three well-defined regions. We find that for $T < T^* = 1.22 T_{c}$ the occurrence of jamming prevents the onset of percolating clusters, while percolation is possible for $T > T^{*}$. Particular attention is focused close to $T^{*}$, where the interplay between jamming and percolation restricts fluctuations, forcing exponents seemingly different from the standard percolation universality class. By analogy with a thermal transition, we study the onset of percolation by using the {\it temperature} (in this case, the substrate annealing temperature) as a control parameter. By proposing thermal scaling Ansatzes we analyze the behavior of the percolation threshold and its thermally induced fluctuations. Also, the fractal dimension of the percolating cluster is determined. Based on these measurements and the excellent data collapsing, we conclude that the universality class of standard percolation is preserved for all temperatures.