A lattice ribbon is a connected sequence of plaquettes subject to certain self-avoidance conditions. The ribbon can be closed to form an object which is topologically either a cylinder or a Mobius band, depending on whether its surface is orientable or nonorientable. We describe a grand canonical Monte Carlo algorithm for generating a sample of these ribbons, prove that the associated Markow chain is ergodic, and present and discuss numerical results about the dimensions and entanglement complexity of the ribbons.
A Monte Carlo algorithm for lattice ribbons
ORLANDINI, ENZO;
1996
Abstract
A lattice ribbon is a connected sequence of plaquettes subject to certain self-avoidance conditions. The ribbon can be closed to form an object which is topologically either a cylinder or a Mobius band, depending on whether its surface is orientable or nonorientable. We describe a grand canonical Monte Carlo algorithm for generating a sample of these ribbons, prove that the associated Markow chain is ergodic, and present and discuss numerical results about the dimensions and entanglement complexity of the ribbons.
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