Geometric Exponents of Dilute Logarithmic Minimal Models

Details Geometric Exponents of Dilute Logarithmic Minimal Models Geometric Exponents of Dilute Logarithmic Minimal Models

2011-09-03

arxiv.org/abs/1109.0653v1

Physics

Condensed Matter

Statistical Mechanics

41 pages, 32 figures, added references

Scientific paper

The fractal dimensions of the hull, the external perimeter and of the red bonds are measured through Monte Carlo simulations for dilute minimal models, and compared with predictions from conformal field theory and SLE methods. The dilute models used are those first introduced by Nienhuis. Their loop fugacity is beta = -2cos(pi/barkappa}) where the parameter barkappa is linked to their description through conformal loop ensembles. It is also linked to conformal field theories through their central charges c = 13 - 6(barkappa + barkappa^{-1}) and, for the minimal models of interest here, barkappa = p/p' where p and p' are two coprime integers. The geometric exponents of the hull and external perimeter are studied for the pairs (p,p') = (1,1), (2,3), (3,4), (4,5), (5,6), (5,7), and that of the red bonds for (p,p') = (3,4). Monte Carlo upgrades are proposed for these models as well as several techniques to improve their speeds. The measured fractal dimensions are obtained by extrapolation on the lattice size H,V -> infinity. The extrapolating curves have large slopes; despite these, the measured dimensions coincide with theoretical predictions up to three or four digits. In some cases, the theoretical values lie slightly outside the confidence intervals; explanations of these small discrepancies are proposed.

Affiliated with

Also associated with

No associations

Rating

Geometric Exponents of Dilute Logarithmic Minimal Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometric Exponents of Dilute Logarithmic Minimal Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric Exponents of Dilute Logarithmic Minimal Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-108781