Physical Review E
We extend the model of a 2d 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 three- and four-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.
Diep, H. T. and Kaufman, Miron, "Extended Defects in the Potts-Percolation Model of a Solid: Renormalization Group and Monte Carlo Analysis" (2009). Physics Faculty Publications. 113.
Diep, H. T. and Miron Kaufman. "Extended Defects in the Potts-Percolation Model of a Solid: Renormalization Group and Monte Carlo Analysis." Physical Review E 80 (2009): 31116.
Copyright 2009 American Physical Society. Available on publisher's site at http://pre.aps.org/abstract/PRE/v80/i3/e031116.