Extended Defects in the Potts-Percolation Model of a Solid: Renormalization Group and Monte Carlo Analysis

TL;DR

This paper investigates the effects of line defects in a 2D solid model, combining renormalization group theory and Monte Carlo simulations to analyze phase transitions and defect behavior.

Contribution

It introduces a model with line defects in a 2D solid and combines RG and Monte Carlo methods to study defect effects on phase transitions.

Findings

Elastic energy is irrelevant at the bulk critical point.

Discontinuous change in defect line order parameter for strong defect interactions.

Continuous variation of defect energy at the bulk critical temperature.

Abstract

We extend the model of a 2$d$ solid to include a line of defects. Neighboring atoms on the defect line are connected by ?springs? of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization group we show that the elastic energy is an irrelevant field at the bulk critical point. For zero elastic energy this model reduces to the Potts model. By using Monte Carlo simulations of the 3- and 4-state Potts model on a square lattice with a line of defects, we confirm the renormalization-group prediction that for a defect interaction larger than the bulk interaction the order parameter of the defect line changes discontinuously while the defect energy varies continuously as a function of temperature at the bulk critical temperature.