Thermal Percolation for Interacting Monomers Adsorbed on Square Lattices

TL;DR

This study investigates how interacting monomers percolate on a square lattice, analyzing critical behavior, phase diagrams, and the influence of interactions, revealing universal percolation properties despite different interaction types.

Contribution

The paper provides a detailed finite-size scaling analysis and phase diagram for interacting monomers on a square lattice, highlighting the universality class of the percolation transition.

Findings

Critical exponents consistent with random percolation.

Phase diagram delineates percolating and non-percolating regions.

Surface coverage scaling maintains universality class.

Abstract

In this paper the percolation of monomers on a square lattice is studied as the particles interact with either repulsive or attractive energies. By means of a finite-size scaling analysis, the critical exponents and the scaling collapsing of the fraction of percolating lattice are found. A phase diagram separating a percolating from a non-percolating region is determined. The main features of the phase diagram are discussed in terms of simple considerations related to the interactions present in the problem. The influence of the phase transitions occurring in the system is reflected by the phase diagram. In addition, a scaling treatment maintaining constant the surface coverage and varying the temperature of the system is performed. In all the considered cases, the universality class of the model is found to be the same as for the random percolation model.