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PhysRevE.91.022133.pdf (1.62 MB)

Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization

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posted on 2023-06-09, 13:43 authored by Dhagash Mehta, Jonathan D Hauenstein, Matthew Niemerg, Nicholas SimmNicholas Simm, Daniel A Stariolo
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Physical Review E (PRE)

ISSN

1539-3755

Publisher

American Physical Society

Volume

91

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-06-13

First Open Access (FOA) Date

2018-06-13

First Compliant Deposit (FCD) Date

2019-07-02

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