Roughening of k-mer-growing interfaces in stationary regimes

Area of Science:

• Statistical mechanics
• Surface growth phenomena
• Condensed matter physics

Background:

• Solid-on-solid growth models are crucial for understanding surface evolution.
• Periodic boundary conditions are often used to simplify simulations of large systems.
• Extended particles (dimers, trimers, etc.) introduce complexity beyond simple monomer aggregation.

Purpose of the Study:

• To analyze the steady-state dynamics of interfaces in 1+1 dimensional solid-on-solid growth models.
• To investigate the role of extended particle aggregation (k-mers) on interface roughening.
• To determine if universal scaling behaviors observed in monomer systems extend to systems with extended particles.

Main Methods:

• Mapping the interface dynamics to an asymmetric simple exclusion process (ASEP).
• Utilizing k-type vacancies within the ASEP framework to represent extended particles.
• Direct evaluation of roughening exponents, width, and maximal height distributions in stationary regimes.

Main Results:

• The dynamics can be partitioned into numerous sectors for k≥2.
• Roughening exponents and height distributions were evaluated.
• Generic cases exhibit scaling behavior closely resembling that of monomer interfaces.

Conclusions:

• The study provides a method to analyze complex interface dynamics via ASEP.
• Universal scaling behavior appears to be a robust feature, persisting even with extended particles.
• Findings contribute to the understanding of surface growth universality classes.