Critical behavior of repulsive linear $k$-mers on triangular lattices

TL;DR

This study investigates the critical behavior of repulsive linear $k$-mers on a triangular lattice, revealing phase transitions and critical exponents for $k$ between 1 and 3, and comparing Monte Carlo results with theoretical predictions.

Contribution

It provides new insights into the critical phenomena of $k$-mers on lattices, including critical temperature dependence and universality class distinctions for different $k$ values.

Findings

Identification of a finite-temperature order-disorder phase transition.

Quantitative agreement between MC simulations and FEMCA predictions.

Critical exponents determined for $k=1$ to $k=3$, showing deviation from Potts model universality.

Abstract

Monte Carlo (MC) simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer two-dimensional gas of repulsive linear $k$-mers on a triangular lattice at coverage $k/(2k+1)$. A low-temperature ordered phase, characterized by a repetition of alternating files of adsorbed $k$-mers separated by $k+1$ adjacent empty sites, is separated from the disordered state by a order-disorder phase transition occurring at a finite critical temperature, $T_c$. The MC technique was combined with the recently reported Free Energy Minimization Criterion Approach (FEMCA), [F. Rom\'a et al., Phys. Rev. B, 68, 205407, (2003)], to predict the dependence of the critical temperature of the order-disorder transformation. The dependence on $k$ of the transition temperature, $T_c(k)$, observed in MC is in qualitative agreement with FEMCA. In addition, an accurate determination of the critical exponents has been obtained for adsorbate sizes ranging between $k=1$ and $k=3$. For $k>1$, the results reveal that the system does not belong to the universality class of the two-dimensional Potts model with $q=3$ ($k=1$, monomers). Based on symmetry concepts, we suggested that the behavior observed for $k=1, 2$ and 3 could be generalized to include larger particle sizes ($k \geq 2$).