The thesis is organized as follows. In the rest of this introductory chapter we review in more detail the main relevant experiments, and point to some implications of these for our model building. Chapter 2 is devoted to a general discussion of models to be treated in subsequent chapters. First we recall the well-known displacive versus orderdisorder regime aspects of the standard classical model for structural phase transitions, and discuss the extent to which these aspects pertain to the case of QPE perovskites. Correspondingly, we divide the possible models into two classes, those based on continuous and those based on discrete degrees of freedom. As an example of the former class, we propose a Landau-Ginzburg-Wilson hamiltonian for SrTi03 , including elastic couplings, which leads to discuss the existence of an incommensurate phase. Considering the latter class of models, we try to identify their most important ingredients, taking as relevant degrees of freedom the discrete Ti - 0 bond variables. In Chapter 3, the classical incommensurate ferroelectricity arising from elastic couplings is investigated in detail, and the effect of quantum fluctuations is discussed on a heuristic level. In Chapter 4 we then investigate three idealized 2D quantum discrete lattice models. The first is a plain quantum four-state clock model, while the second includes an ice-type constraint. Both models are studied by means of a numerical Path Integral Monte Carlo simulation (PIMC), and the corresponding phase diagrams are determined with reasonable accuracy. On the technical side, in order to overcome the pathologically slow 1 / m convergence in number of Trotter slices in case of the constrained model, a special method has been invented, which is described in detail in Appendix A. In the last section of chapter 4 we describe our third model, which consists of endowing the constrained four-state clock model with an additional physical effect, namely the possibility of bond hopping and 'bond vacancies'. For this third model we have so far not been able to set up an accurate numerical simulation technique, allowing us to determine the complete phase diagram in the parameter space at finite temperatures. Some general considerations are presented, based on analogies with Andreev and Lifshitz's work [18] on quantum crystals of H e^4 , whose main idea is briefly summarized in Appendix B, for the sake of completeness. A particular zero temperature and zero coupling case of this more complete third model is studied numerically, by means of a Variational Monte Carlo technique, the details of which are described in Appendix C. Finally the last, fifth, chapter is devoted to discussion and conclusions.

Models of quantum paraelectric behaviour of perovskites / Martonak, Roman. - (1993 Oct 29).

Models of quantum paraelectric behaviour of perovskites

Martonak, Roman
1993

Abstract

The thesis is organized as follows. In the rest of this introductory chapter we review in more detail the main relevant experiments, and point to some implications of these for our model building. Chapter 2 is devoted to a general discussion of models to be treated in subsequent chapters. First we recall the well-known displacive versus orderdisorder regime aspects of the standard classical model for structural phase transitions, and discuss the extent to which these aspects pertain to the case of QPE perovskites. Correspondingly, we divide the possible models into two classes, those based on continuous and those based on discrete degrees of freedom. As an example of the former class, we propose a Landau-Ginzburg-Wilson hamiltonian for SrTi03 , including elastic couplings, which leads to discuss the existence of an incommensurate phase. Considering the latter class of models, we try to identify their most important ingredients, taking as relevant degrees of freedom the discrete Ti - 0 bond variables. In Chapter 3, the classical incommensurate ferroelectricity arising from elastic couplings is investigated in detail, and the effect of quantum fluctuations is discussed on a heuristic level. In Chapter 4 we then investigate three idealized 2D quantum discrete lattice models. The first is a plain quantum four-state clock model, while the second includes an ice-type constraint. Both models are studied by means of a numerical Path Integral Monte Carlo simulation (PIMC), and the corresponding phase diagrams are determined with reasonable accuracy. On the technical side, in order to overcome the pathologically slow 1 / m convergence in number of Trotter slices in case of the constrained model, a special method has been invented, which is described in detail in Appendix A. In the last section of chapter 4 we describe our third model, which consists of endowing the constrained four-state clock model with an additional physical effect, namely the possibility of bond hopping and 'bond vacancies'. For this third model we have so far not been able to set up an accurate numerical simulation technique, allowing us to determine the complete phase diagram in the parameter space at finite temperatures. Some general considerations are presented, based on analogies with Andreev and Lifshitz's work [18] on quantum crystals of H e^4 , whose main idea is briefly summarized in Appendix B, for the sake of completeness. A particular zero temperature and zero coupling case of this more complete third model is studied numerically, by means of a Variational Monte Carlo technique, the details of which are described in Appendix C. Finally the last, fifth, chapter is devoted to discussion and conclusions.
Tosatti, Erio
Martonak, Roman
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/4058
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