QUENCHING DYNAMICS OF SPIN SYSTEMS WITH DISCRETE SYMMETRY: A GATEWAY TO STUDY OPINION DYNAMICS WITH MULTIPLE DISCRETE OPINION

Victor Hugo, Martin Del Campo Moreno

Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12104/92064

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DC Field	Value	Language
dc.contributor.author	Victor Hugo, Martin Del Campo Moreno
dc.date.accessioned	2023-04-19T18:50:57Z	-
dc.date.available	2023-04-19T18:50:57Z	-
dc.date.issued	2019-05-31
dc.identifier.uri	https://wdg.biblio.udg.mx
dc.identifier.uri	https://hdl.handle.net/20.500.12104/92064	-
dc.description.abstract	A magnetic system is a set of magnetic dipoles, often called spins, where each one is a vertex of a lattice. In these kinds of systems, the spins might interact with each others in diferent ways, being able to exchange energy. The diferent ways the spins interact on the system results in diferent models. In these systems, there is a measure of the order in the system called order parameter. The value of the order parameter is 1 when the system is in complete order and 0 when it is in complete disorder. For example, in ferromagnetic interaction, the order parameter is usually the magnetization. We will study the dynamics of discrete spin systems. The phenomena in which the temperature of a system is suddenly dropped from a very high temperature to a very low temperature without allowing real time to change are known as quenching dynamics
dc.description.tableofcontents	1 Introduction 1 1.1 Models and dynamics for spin systems. . . . . . . . . . . . . . . . . . . . . . 1 1.2 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Spin models........................................................4 2.1 Ising model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The Potts model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Standard Potts model . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Planar Potts model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.3 Two-state Potts model: Ising model . . . . . . . . . . . . . . . . . . 7 3 Features of quenching dynamics 9 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Dynamical rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2.1 Glauber dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2.2 Equivalence between planar and standard Potts model . . . . . . . . 12 3.2.3 Social pressure dynamics. . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 Measurements and evolution of the system . . . . . . . . . . . . . . . . . . . 16 3.3.1 Domain coarsening and magnetization . . . . . . . . . . . . . . . . . 16 3.3.2 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3.3 Persistence and nite size scaling . . . . . . . . . . . . . . . . . . . . 19 3.3.4 Exit probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.1 Glauber dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.1.1 Domain walls and dynamical exponent z . . . . . . . . . . . . . . . . 23 4.1.2 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.1.3 Persistence probability . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.1.4 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.1.5 Exit probability E(x) . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2 Social pressure dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2.1 Domain walls decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2.2 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2.3 Persistence probability . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.2.4 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2.5 Exit probability E(x) . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5 Conclusions and discussions ..... . .. . . .. . . . . .. . ......46 5.1 Glauber dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.2 Social pressure dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 A.1 Glauber dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 A.1.1 Domain walls and dynamical exponent z . . . . . . . . . . . . . .. 48 A.1.2 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 A.1.3 Persistence probability . . . . . . . . . . . . . . . . . . . . . . . . . . 51 A.1.4 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 A.2 Social pressure dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 54 A.2.1 Domain walls and dynamical exponent z . . . . . . . . . . . . . . . . 54 A.2.2 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 A.2.3 Persistence probability . . . . . . . . . . . . . . . . . . . . . . . . . . 57 A.2.4 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
dc.format	application/PDF
dc.language.iso	eng
dc.publisher	Biblioteca Digital wdg.biblio
dc.publisher	Universidad de Guadalajara
dc.rights.uri	https://www.riudg.udg.mx/info/politicas.jsp
dc.subject	Dipolos
dc.subject	Spins
dc.subject	The Phenomena
dc.title	QUENCHING DYNAMICS OF SPIN SYSTEMS WITH DISCRETE SYMMETRY: A GATEWAY TO STUDY OPINION DYNAMICS WITH MULTIPLE DISCRETE OPINION
dc.type	Tesis de Licenciatura
dc.rights.holder	Universidad de Guadalajara
dc.rights.holder	Victor Hugo, Martin Del Campo Moreno
dc.coverage	GUADALAJARA, JALISCO.
dc.type.conacyt	bachelorThesis
dc.degree.name	LICENCIATURA EN FISICA
dc.degree.department	CUCEI
dc.degree.grantor	Universidad de Guadalajara
dc.rights.access	openAccess
dc.degree.creator	LICENCIADO EN FISICA
dc.contributor.director	Soham, Biswas
Appears in Collections:	CUCEI

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