Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-05-17
Phys. Rev. E 80 (2009) 031116
Physics
Condensed Matter
Statistical Mechanics
13 figures, 17 pages
Scientific paper
10.1103/PhysRevE.80.031116
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.
Diep Hung-The
Kaufman Miron
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