Criticality Eight Vertices Model Neighborhood Soluble Models Higher Lower Quotas Method

Author(s)

Claudio Fernandes de Souza Rodrigues

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2003-12-15

Examining board members

Domingos Humberto Urbano Marchetti; Henrique Von Dreifus; Paulo Afonso Faria da Veiga; Walter Felipe Wreszinski; Carlos Seihiti Orii Yokoi

• Advisor: Domingos Humberto Urbano Marchetti

Abstract

The aim of this work is to analyze the behavior of critical exponents in the eight-vertex model starting from the upper and lower bound obtained for its partition function. We studied the quantum onedimensional Heisenberg model also denominated XYZh model. We propose na alternative way of approaching universality in Heisenberg and Ising models using inequalities satisfied for their partition functions.Among the methods that we used in the solutions of the models atand out the integration on the Grassmann variables, the mapping of a onedimensional model in a two-dimensional one through the aid of the Trotter formula and, finally, the representation of the partition function as Pfaffian of a matrix. To obtain na upper bound, the positivity reflection technique was used, extended to the case of variables that, anticomute, and the method of thechess board estimate. (AU)