Doctoral Dissertations

Keywords and Phrases

Critical behavior; Disorder; Magnetic systems; Monte Carlo Methods; Quantum phase transitions

Abstract

This work examines the effects of quenched disorder on classical and quantum phase transitions. There are countless examples of phase transitions in nature. Here, we study phase transitions in condensed matter with the help of simple models that focus on the essential unifying features of the problems. We are particularly interested in investigating how the presence of disorder changes the behavior of the system in the vicinity of a phase transition.

Here, we discuss three closely related problems regarding phase transitions. First we consider the behavior of highly diluted magnets with varying dilution levels in order to explain the unusual phase diagram observed in experiments on hexaferrite materials through a percolation scenario. Next, we study the response of a two-dimensional planar (XY) magnet to a finite twist in the boundary conditions. Such boundary conditions are important for numerous experimental scenarios and computational methods. Then, we investigate the phase diagram of the disordered quantum clock model in one dimension. This system exhibits multiple phases and phase transitions that are strongly affected by disorder.

To understand the phase transitions in the above systems, we analyze the equilibrium properties of thermodynamic observables using large-scale Monte Carlo simulations. The utility of the simulations is further enhanced by a sophisticated finite-size scaling analysis. Our research presents a comprehensive analysis of the disorder dependence of phases and phase transitions in the aforementioned systems. Through rigorous investigation, we demonstrate that disorder gives rise to a diverse array of novel phenomena. These include alterations in universality class, the emergence of infinite randomness criticality, and Griffiths singularities.

Advisor(s)

Vojta, Thomas

Committee Member(s)

Adrian Del Maestro; Aleksandr Chernatynskiy; Alexey Yamilov; Julia Medvedeva

Department(s)

Physics

Degree Name

Ph. D. in Physics

Publisher

Missouri University of Science and Technology

Publication Date

Summer 2025

Journal article titles appearing in thesis/dissertation

Paper I: Pages 33-58 has been published as Phase boundary near a magnetic percolation transition in The European Physical Journal B, 94, 43 (2021) with Cameron Lerch and Thomas Vojta.
Paper II: Pages 59-88 has been published as Helicity modulus and chiral symmetry breaking for boundary conditions with finite twist in Physical Review E 111, 024114 (2025) with Thomas Vojta.
Paper III: Pages 89-143 has been published as Phases and phase transitions of the disordered quantum clock model in Physical Review B 111, 094212 (2025) with Vishnu Pulloor Kuttanikkad, Rajesh Narayanan and Thomas Vojta.

Pagination

xii, 149 pages

Note about bibliography

Includes_bibliographical_references_(pages 147-148)

Rights

© 2025 Gaurav Ramesh Khairnar , All Rights Reserved

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 12511

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Physics Commons

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