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Doctoral Thesis
DOI
10.11606/T.43.1995.tde-13122013-180031
Document
Author
Full name
Ricardo Andreas Sauerwein
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1995
Supervisor
Committee
Oliveira, Mario Jose de (President)
Antonelli, Alex
Moreira, Francisco Brady
Oliveira, Paulo Murilo Castro de
Salinas, Silvio Roberto de Azevedo
Title in Portuguese
Método de Monte Carlo para Sistemas Quânticos
Keywords in Portuguese
Entropia residual
Física do estado sólido
Mecânica estatística
Modelo de Heisenberg
Sistemas quânticos de spin
Abstract in Portuguese
As propriedades do estado fundamental do modelo de Heisenberg antiferroinagnético quântico de spin-1/2 na rede quadrada e na rede cúbica espacialmente anisotrópica são investigadas através de um novo método de Monte Carlo, baseado na estimativa do maior autovalor de uma matriz de elementos não negativos. A energia do estado fundamental e a magnetização "staggered" destes sistemas são calculadas em redes relativamente grandes com até 24 x 24 sítios para o caso de redes quadradas e 8 x 8 x 8 sítios para o caso de redes cúbicas. O método desenvolvido também pode ser usado como um novo algoritmo para a determinação direta da entropia de sistemas de spins de Ising através de simulações usuais de Monte Carlo. Usando este método, calculamos a entropia do antiferromagneto de Ising na presença de um campo magnético externo nas redes triangular e cúbica de face centrada.
Title in English
Monte Carlo method for quantum systems
Keywords in English
Heisenberg model
Physics of the solid state
Quantum spin systems
Residual entropy
Statistical mechanics
Abstract in English
The ground state properties of the antiferromagnetic quantum Heisenberg model with spin-112 defined on a square lattice and on a cubic lattice with spatial anisotropy are investigated through a new Monte Carlo method, based on the estimation of the largest eigenvalue of a matrix with nonnegative elements. The ground state energy and the staggered magnetization of these systems are calculated in relatively large lattices with up to 24 x 24 sites for the square lattices and 8 x 8 x 8 sites for cubic lattices. The method developped can also be used as a new algorithm for the direct determination of the entropy of Ising spin systems through ordinary Monte Car10 simulations. By using this method we calculate the entropy of the Ising antiferromagnetic in the presence of a magnetic field in the triangular and face centered cubic lattices.
 
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46013Sauerwein.pdf (38.77 Mbytes)
Publishing Date
2014-02-21
 
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