This title appears in the Scientific Report :
2005
Please use the identifier:
http://hdl.handle.net/2128/2367 in citations.
Please use the identifier: http://dx.doi.org/10.1103/PhysRevE.71.065104 in citations.
Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces
Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces
Lattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of two-dimensional site animals on square and triangular lattices in nontrivial geometries. The simulations are done with the pruned-enriched Rosenbluth method (PER...
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Personal Name(s): | Hsu, H. P. |
---|---|
Nadler, W. / Grassberger, P. | |
Contributing Institute: |
John von Neumann - Institut für Computing; NIC |
Published in: | Physical Review E Physical review / E, 71 71 (2005 2005) 6 6, S. 065104 065104 |
Imprint: |
College Park, Md.
APS
2005
2005-06-24 2005-06-01 |
Physical Description: |
065104 |
DOI: |
10.1103/PhysRevE.71.065104 |
Document Type: |
Journal Article |
Research Program: |
Betrieb und Weiterentwicklung des Höchstleistungsrechners |
Series Title: |
Physical Review E
71 |
Subject (ZB): | |
Link: |
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Publikationsportal JuSER |
Please use the identifier: http://dx.doi.org/10.1103/PhysRevE.71.065104 in citations.
Lattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of two-dimensional site animals on square and triangular lattices in nontrivial geometries. The simulations are done with the pruned-enriched Rosenbluth method (PERM) algorithm, which gives very precise estimates of the partition sum, yielding precise values for the entropic exponent theta (Z(N)similar to mu(N)N(-theta)). In particular, we studied animals grafted to the tips of wedges with a wide range of angles alpha, to the tips of cones (wedges with the sides glued together), and to branching points of Riemann surfaces. The latter can either have k sheets and no boundary, generalizing in this way cones to angles alpha > 360 degrees, or can have boundaries, generalizing wedges. We find conformal invariance behavior, theta similar to 1/alpha, only for small angles (alpha << 2 pi), while theta approximate to const-alpha/2 pi for alpha >> 2 pi. These scalings hold both for wedges and cones. A heuristic (nonconformal) argument for the behavior at large alpha is given, and comparison is made with critical percolation. |