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Por favor, use este identificador para citar o enlazar este ítem: https://hdl.handle.net/20.500.12104/96518
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dc.contributor.authorHernandez Gallegos, Dalia Jazmin
dc.date.accessioned2023-11-10T21:14:47Z-
dc.date.available2023-11-10T21:14:47Z-
dc.date.issued2023-06-01
dc.identifier.urihttps://wdg.biblio.udg.mx
dc.identifier.urihttps://hdl.handle.net/20.500.12104/96518-
dc.description.abstractAbstract In this thesis, we have studied two different models of global spin exchange in one dimension for the Ising spin system. In one of the models, the spins interact with their nearest neighbours and both nearest and next nearest neighbours. In the second model the spins interact with their two nearest domains. The critical dynamics of the spin systems is studied with measurables as the fraction of domain walls and the persistence probability. Persistence for the global spin exchange dynamics is studied for the first time. In addition, a study if the persistent sites are forming a fractal is presented. The fractal dimension is obtained through the box counting method and the distribution of the distances between the domains of persistent sites. Furthermore, the two-point correlation of the persistent sites and its scaling behaviour is analysed.
dc.description.tableofcontentsContents List of figures ii List of symbols iv Abstract 1 Introduction 2 1 Chapter 1. Background and theoretical framework 5 1.1 Ising model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Non-equilibrium dynamics of the Ising model . . . . . . . . . . . . . . . . . 6 1.3 Conserved dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 Schelling model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.2 Domain size-dependent global spin exchange dynamics . . . . . . . 11 1.3.3 Details of the dynamics: . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Chapter 2. Methodology and measurables 14 2.1 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Domain coarsening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Persistence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 Two-point correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.2 Scaling laws for the measurables related to persistence . . . . . . . 17 2.3.3 Fractal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3.4 Box counting method . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.5 Distribution of the distances between domains of the persistent sites 22 i 2.4 Simulation details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Chapter 3. Results and analysis 24 3.1 Schelling model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Domain size-dependent dynamics . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.1 Evolution of the domain size-dependent dynamics . . . . . . . . . . 28 3.2.2 Spatial structure of the persistent sites . . . . . . . . . . . . . . . . 30 4 Chapter 4. Discussion 37 4.1 Discussion about the Schelling model . . . . . . . . . . . . . . . . . . . . . 37 4.2 Discussion about the domain size-dependent dynamics . . . . . . . . . . . 39 4.2.1 On α and z2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.2.2 On the average of the distances between domains of the persistent sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5 Chapter 5. Conclusions and further directions 43 5.1 On the Schelling model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2 On the domain size-dependent dynamics . . . . . . . . . . . . . . . . . . . 44 5.3 Further directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Bibliography 46
dc.formatapplication/PDF
dc.language.isoeng
dc.publisherBiblioteca Digital wdg.biblio
dc.publisherUniversidad de Guadalajara
dc.rights.urihttps://www.riudg.udg.mx/info/politicas.jsp
dc.subjectCoarsenning
dc.subjectAnd Fractal Formation In Persistence
dc.titleA NEW OF SPIN SXCHANGE DYNAMICS:COARSENING AND FRACTAL FORMATION IN PERSISTENCE
dc.typeTesis de Maestría
dc.rights.holderUniversidad de Guadalajara
dc.rights.holderHernandez Gallegos, Dalia Jazmin
dc.coverageGUADALAJARA JALISCO
dc.type.conacytmasterThesis
dc.degree.nameMAESTRIA EN CIENCIAS EN FISICA
dc.degree.departmentCUCEI
dc.degree.grantorUniversidad de Guadalajara
dc.rights.accessopenAccess
dc.degree.creatorMAESTRO EN CIENCIAS EN FISICA
dc.contributor.directorBiswas, Soham
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