Chengxiang Ding et al 2007 J. Phys. A: Math. Theor. 40 3305 doi:10.1088/1751-8113/40/13/001
Chengxiang Ding1, Youjin Deng2, Wenan Guo1, Xiaofeng Qian3 and Henk W J Blöte3,4
Show affiliationsWe study the fractal geometry of O(n) loop configurations in two dimensions by means of scaling and a Monte Carlo method, and compare the results with predictions based on the Coulomb gas technique. The Monte Carlo algorithm is applicable to models with noninteger n and uses local updates. Although these updates typically lead to nonlocal modifications of loop connectivities, the number of operations required per update is only of order 1. The Monte Carlo algorithm is applied to the honeycomb O(n) model for several values of n, including noninteger ones. We thus determine scaling exponents that describe the fractal nature of O(n) loops at criticality. The results of the numerical analysis agree with the theoretical predictions.
02.40.-k Geometry, differential geometry, and topology
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
Issue 13 (30 March 2007)
Received 28 November 2006, in final form 7 February 2007
Published 14 March 2007
Chengxiang Ding et al 2007 J. Phys. A: Math. Theor. 40 3305
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