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Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization
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Mehta, Dhagash, Hauenstein, Jonathan D., Niemerg, Matthew, Simm, Nick and Stariolo, Daniel A. (2015) Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 91 (2). 022133. doi:10.1103/PhysRevE.91.022133 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.91.022133
Abstract
Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical study of the finite size 2-spin spherical model using both numerical polynomial homotopy continuation and a reformulation via non-hermitian matrices. The continuation approach computes all of the complex stationary points of this model while the matrix approach computes the real stationary points. Using these methods, we compute the average number of stationary points while changing the topology of the PEL as well as the variance. Histograms of these stationary points are presented along with an analysis regarding the complex stationary points. This work connects topology trivialization to two different branches of mathematics: algebraic geometry and catastrophe theory, which is fertile ground for further interdisciplinary research.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Topology, Geometry, Algebraic, Catastrophes (Mathematics) | ||||||||
| Journal or Publication Title: | Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) | ||||||||
| Publisher: | American Physical Society | ||||||||
| ISSN: | 1539-3755 | ||||||||
| Official Date: | 23 February 2015 | ||||||||
| Dates: |
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| Volume: | 91 | ||||||||
| Number: | 2 | ||||||||
| Article Number: | 022133 | ||||||||
| DOI: | 10.1103/PhysRevE.91.022133 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 8 March 2017 | ||||||||
| Date of first compliant Open Access: | 8 March 2017 | ||||||||
| Funder: | United States. Defense Advanced Research Projects Agency (DARPA), Simons Institute for the Theory of Computing, National Institute for Mathematical Sciences (South Korea) (NIMS), Centre for Applications of Mathematical Principles (South Korea) (CAMP), Conselho Nacional de Desenvolvimento CientÃfico e Tecnológico (CNPq), Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
| Grant number: | EP/J002763/1 (EPSRC) |
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