Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement
Abstract We perform Monte Carlo simulations to determine the critical temperatures of Ising Ferromagnets (IFM) on different types of two-dimensional proximity graphs, in which the distribution of their underlying node sets has been changed systematically by means of a parameter σ. This allows us to...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2017-08-01
|
| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-017-08531-8 |
| _version_ | 1818994853427544064 |
|---|---|
| author | Hendrik Schawe Christoph Norrenbrock Alexander K. Hartmann |
| author_facet | Hendrik Schawe Christoph Norrenbrock Alexander K. Hartmann |
| author_sort | Hendrik Schawe |
| collection | DOAJ |
| description | Abstract We perform Monte Carlo simulations to determine the critical temperatures of Ising Ferromagnets (IFM) on different types of two-dimensional proximity graphs, in which the distribution of their underlying node sets has been changed systematically by means of a parameter σ. This allows us to interpolate between regular grids and proximity graphs based on complete random placement of nodes. Each edge of the planar proximity graphs carries a weighted ferromagnetic coupling. The coupling strengths are determined via the Euclidean distances between coupled spins. The simulations are carried out on graphs with N = 162 to N = 1282 nodes utilising the Wolff cluster algorithm and parallel tempering method in a wide temperature range around the critical point to measure the Binder cumulant in order to obtain the critical temperature for different values of σ. Interestingly, the critical temperatures depend partially non-monotonously on the disorder parameter σ, corresponding to a non-monotonous change of the graph structure. For completeness, we further verify using finite-size scaling methods that the IFM on proximity graphs is for all values of the disorder in the same universality class as the IFM on the two-dimensional square lattice. |
| first_indexed | 2024-12-20T21:04:33Z |
| format | Article |
| id | doaj.art-1525418e28ff4f36bf7d71aea6874317 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-12-20T21:04:33Z |
| publishDate | 2017-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-1525418e28ff4f36bf7d71aea68743172022-12-21T19:26:37ZengNature PortfolioScientific Reports2045-23222017-08-01711810.1038/s41598-017-08531-8Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node PlacementHendrik Schawe0Christoph Norrenbrock1Alexander K. Hartmann2Institut für Physik, Universität OldenburgInstitut für Physik, Universität OldenburgInstitut für Physik, Universität OldenburgAbstract We perform Monte Carlo simulations to determine the critical temperatures of Ising Ferromagnets (IFM) on different types of two-dimensional proximity graphs, in which the distribution of their underlying node sets has been changed systematically by means of a parameter σ. This allows us to interpolate between regular grids and proximity graphs based on complete random placement of nodes. Each edge of the planar proximity graphs carries a weighted ferromagnetic coupling. The coupling strengths are determined via the Euclidean distances between coupled spins. The simulations are carried out on graphs with N = 162 to N = 1282 nodes utilising the Wolff cluster algorithm and parallel tempering method in a wide temperature range around the critical point to measure the Binder cumulant in order to obtain the critical temperature for different values of σ. Interestingly, the critical temperatures depend partially non-monotonously on the disorder parameter σ, corresponding to a non-monotonous change of the graph structure. For completeness, we further verify using finite-size scaling methods that the IFM on proximity graphs is for all values of the disorder in the same universality class as the IFM on the two-dimensional square lattice.https://doi.org/10.1038/s41598-017-08531-8 |
| spellingShingle | Hendrik Schawe Christoph Norrenbrock Alexander K. Hartmann Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement Scientific Reports |
| title | Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement |
| title_full | Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement |
| title_fullStr | Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement |
| title_full_unstemmed | Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement |
| title_short | Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement |
| title_sort | ising ferromagnets on proximity graphs with varying disorder of the node placement |
| url | https://doi.org/10.1038/s41598-017-08531-8 |
| work_keys_str_mv | AT hendrikschawe isingferromagnetsonproximitygraphswithvaryingdisorderofthenodeplacement AT christophnorrenbrock isingferromagnetsonproximitygraphswithvaryingdisorderofthenodeplacement AT alexanderkhartmann isingferromagnetsonproximitygraphswithvaryingdisorderofthenodeplacement |