Ising models with competition

Author(s)

Mário Noboru Tamashiro

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 1996-06-28

Examining board members

Silvio Roberto de Azevedo Salinas; Márcia Cristina Bernardes Barbosa; Sérgio Galvão Coutinho; Jose Guilherme Martins Alves Moreira; Carlos Seihiti Orii Yokoi

• Advisor: Silvio Roberto de Azevedo Salinas

Abstract

In this work we consider three Ising models with competition: which is generated by dynamical couplings of antagonistic character, by the geometry of the underlying lattice, or by interactions of competitive uniaxial periodicities and disorder elements. The first model, for which equilibrium statistical mechanics techniques do not apply, consists in a fully connected attractor neural network storing p = 2 patterns, whose temporal evolution can be described (in the case of synchronous updating) by a two-dimensional dissipative mapping. The second model refers to the classic problem of the Ising antiferromagnet on the triangular lattice in the presence of a uniform magnetic field, which is investigated by various approximations - in particular, by a Bethe-Peierls approximation considering three interpenetrating equivalent sublattices. The third model, introduced to investigate the effects of quenched disorder in a modulated magnetic system, is defined by the ANNNI model in a random field. Initially we consider an analogous of this model on a Cayley tree, in the infinite-coordination limit, which can be formulated in terms of a two-dimensional dissipative mapping. Next, we consider a mean-field version on a simple cubic lattice, which allows for an analysis of the first-order transition surfaces and tricritical lines. (AU)