Study of irreversible models; contact process, assimetric sandpile and linear glauber model

Author(s)

Evandro Freire da Silva

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2009-10-23

Examining board members

Mario Jose de Oliveira; Silvio da Costa Ferreira Junior; Jose Guilherme Martins Alves Moreira; Jürgen Fritz Stilck; Andre de Pinho Vieira

• Advisor: Mario Jose de Oliveira

Abstract

In this work we study some reversible and irreversible stochastic models using various techniques that include series expansions, numerical simulations and analytical methods. Firstly we write a supercritical series expansion of the particle density of the one-dimensional contact process, which gives us the critical annihilation rate and critical exponent ¯ after using the Pad´e approximants method. Secondly we examine the assimetric height restricted sandpile model, which presents a non-zero particle flux at the stationary active state and its critical properties are determined as a function of the assimetry parameter p. Finally we study analitically the linear Glauber model, which is identical in one dimension to the Glauber model. It is possible in any dimension to obtain an expression of the susceptibility of the linear Glauber model from a perturbative series expansion in which the coefficients can be determined at all orders. We also discuss how to generalize the method in order to obtain a series expansion for the Glauber model in two dimensions. (AU)