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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Hendrik Schawe, Christoph Norrenbrock, Alexander K. Hartmann
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/1525418e28ff4f36bf7d71aea6874317
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:1525418e28ff4f36bf7d71aea6874317
record_format	dspace
spelling	oai:doaj.org-article:1525418e28ff4f36bf7d71aea68743172021-12-02T16:07:56ZIsing Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement10.1038/s41598-017-08531-82045-2322https://doaj.org/article/1525418e28ff4f36bf7d71aea68743172017-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-08531-8https://doaj.org/toc/2045-2322Abstract 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.Hendrik SchaweChristoph NorrenbrockAlexander K. HartmannNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-8 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Hendrik Schawe Christoph Norrenbrock Alexander K. Hartmann Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement
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.
format	article
author	Hendrik Schawe Christoph Norrenbrock Alexander K. Hartmann
author_facet	Hendrik Schawe Christoph Norrenbrock Alexander K. Hartmann
author_sort	Hendrik Schawe
title	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_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_sort	ising ferromagnets on proximity graphs with varying disorder of the node placement
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/1525418e28ff4f36bf7d71aea6874317
work_keys_str_mv	AT hendrikschawe isingferromagnetsonproximitygraphswithvaryingdisorderofthenodeplacement AT christophnorrenbrock isingferromagnetsonproximitygraphswithvaryingdisorderofthenodeplacement AT alexanderkhartmann isingferromagnetsonproximitygraphswithvaryingdisorderofthenodeplacement
_version_	1718384640072351744

Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement

Ejemplares similares