Diluted Ising model on a Beth lattice

Author(s)

Ricardo Paupitz Barbosa dos Santos

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2002-09-19

Examining board members

Carlos Seihiti Orii Yokoi; Carlos Castilla Becerra; Fernando Dantas Nobre; Joao Antonio Plascak; Silvio Roberto de Azevedo Salinas

• Advisor: Carlos Seihiti Orii Yokoi

Abstract

The site diluted Ising model is studied on a Beth lattice. The hierarchical structure of the Bethe lattice leads naturally to recursion relations obeyed by the probability distributions of the effective fields. The thermodynamic quantities on the Bethe lattice are then explicitly written in terms of the limiting distributions of the effective fields. Numerically exact results (i.e. if we neglect roundoff errors) for the distributions of the effective fields for T = 0 are presented, together with analytic results for select cases. It is found that the number of effective fields is always finite in the case of ferromagnetic interactions , but it might diverge for irrational values of the applied field in the case of antiferromagnetic interactions. These results yeld a numerically exact applied field versus concentration phase diagram for diluted antiferromagnet at T = 0. The distributions of the effective fields are computed aproximately for T > 0 and used to evaluete various thermodynamic quantities. Curves for the magnetization, free energy, internal energy and entropy are displayed. These calculations give an approximate three-dimensional phase diagram in the space of applied field, temperature and concentration. (AU)