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http://hdl.handle.net/1783.1/6571
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| Title: | Phase-space networks of the six-vertex model under different boundary conditions |
| Authors: | Han, Yilong |
| Keywords: | Phase space structures
Six-vertex model |
| Issue Date: | Apr-2010 |
| Citation: | Physical review E, v. 81, iss. 4, 041118, April 2010 |
| Abstract: | The six-vertex model is mapped to three-dimensional sphere stacks and different boundary conditions corresponding to different containers. The shape of the container provides a qualitative visualization of the boundary effect. Based on the sphere-stacking picture, we map the phase spaces of the six-vertex models to discrete networks. A node in the network represents a state of the system, and an edge between two nodes represents a zero-energy spin flip, which corresponds to adding or removing a sphere. The network analysis shows that the phase spaces of systems with different boundary conditions share some common features. We derived a few formulas for the number and the sizes of the disconnected phase-space subnetworks under the periodic boundary conditions. The sphere stacking provides new challenges in combinatorics and may cast light on some two-dimensional models. |
| Rights: | Physical Review E © copyright (2010) American Physical Society. The Journal's web site is located at http://pre.aps.org |
| URI: | http://hdl.handle.net/1783.1/6571 |
| Appears in Collections: | PHYS Journal/Magazine Articles
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| phasespace.pdf | | 1264Kb | Adobe PDF | View/Open |
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