Desarrollo e implementación de métodos de cómputo para densidades de estados, usando ensambles generalizados
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Fecha
2022
Autores
Facultad/escuela
Idioma
es
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ISSN de la revista
Título del volumen
Editor
Universidad Andrés Bello
Nombre de Curso
Licencia CC
Licencia CC
Resumen
El presente trabajo se enfoca en el desarrollo e implementación de algoritmos de simulación que permitan calcular la Densidad de Estados (DOS) de
sistemas de muchas partículas interactuantes usando ensambles generalizados. Métodos para obtener las propiedades de un sistema que se basan en
el uso de ensambles canónicos o microcanónicos—como el popular algoritmo
de Metropolis—se han usado durante ya un largo tiempo. Sin embargo, el
empleo de ensambles generalizados muestra ser una alternativa que permite
generar curvas más suaves con menor número de simulaciones, además de
evitar ciertos problemas típicos de esos métodos como el tener dificultades
para muestrear correctamente sistemas con muchos mínimos locales. En este
trabajo se presenta una implementación flexible y modular del algoritmo de
Wang–Landau, además de un novedoso algoritmo basado en un método Bayesiano para el cálculo directo de la DOS, los cuales puede ser usados para
obtener las propiedades termodinámicas de un sistema con una superficie de
energía potencial compleja. Nuestros resultados muestran que los algoritmos
son capaces de calcular la DOS con razonable precisión. Hemos estudiado,
como aplicación de los métodos anteriormente mencionados, las propiedades
termodinámicas de un modelo de Potts de 3 estados modificado, en el contexto de la aproximación de “lattice gas” para partículas cargadas confinadas
en un volumen.
The present work is focused on the development and implementation of simulation algorithms in order to compute the density of states (DOS) of systems with many interacting particles by using generalized ensembles. Methods for computing the properties of a system based on the use of canonical and microcanonical ensembles—such as the popular Metropolis algorithm—has been used for a long time. However, the use of generalized ensembles has shown to be an alternative that allows the computation of smoother curves in a smaller number of simulations, while avoiding certain typical problems that arise with those methods such as diculties with the correct sampling of systems with many local minima. In this work, a flexible and modular implementation of the Wang–Landau algorithm is presented, in addition to a novel algorithm based on a Bayesian method for the direct computation of the DOS, both of them can be used to obtain the thermodynamic properties of a system with a complex potential energy landscape. Our results show that the algorithms can compute the DOS with reasonable precision. We have studied, as an application of the aforementioned methods, the thermodynamic properties of a modified three-state Potts model, in the context of the “lattice gas” approximation for charged particles confined in a volume.
The present work is focused on the development and implementation of simulation algorithms in order to compute the density of states (DOS) of systems with many interacting particles by using generalized ensembles. Methods for computing the properties of a system based on the use of canonical and microcanonical ensembles—such as the popular Metropolis algorithm—has been used for a long time. However, the use of generalized ensembles has shown to be an alternative that allows the computation of smoother curves in a smaller number of simulations, while avoiding certain typical problems that arise with those methods such as diculties with the correct sampling of systems with many local minima. In this work, a flexible and modular implementation of the Wang–Landau algorithm is presented, in addition to a novel algorithm based on a Bayesian method for the direct computation of the DOS, both of them can be used to obtain the thermodynamic properties of a system with a complex potential energy landscape. Our results show that the algorithms can compute the DOS with reasonable precision. We have studied, as an application of the aforementioned methods, the thermodynamic properties of a modified three-state Potts model, in the context of the “lattice gas” approximation for charged particles confined in a volume.
Notas
Tesis (Doctor en Ciencias Físicas)
Palabras clave
Algoritmos de Simulación, Densidad de Estados (Física)