PhysRevE.91.022133.pdf (1.62 MB)
Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization
journal contribution
posted on 2023-06-09, 13:43 authored by Dhagash Mehta, Jonathan D Hauenstein, Matthew Niemerg, Nicholas SimmNicholas Simm, Daniel A StarioloMotivated 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.
History
Publication status
- Published
File Version
- Published version
Journal
Physical Review E (PRE)ISSN
1539-3755Publisher
American Physical SocietyExternal DOI
Volume
91Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes