Doctoral Dissertations

Keywords and Phrases

Contact Process; Critical Behavior; Nonequilibrium Phase Transition; Quantum First-order; Quasiperiodic Modulations; Topological Disorder


"In this thesis we study the effects of different types of disorder and quasiperiodic modulations on quantum, classical and nonequilibrium phase transitions. After a brief introduction, we examine the effect of topological disorder on phase transitions and explain a host of violations of the Harris and Imry-Ma criteria that predict the fate of disordered phase transitions. We identify a class of random and quasiperiodic lattices in which a topological constraint introduces strong anticorrelations leading to modifications of the Harris and Imry-Ma criteria for such lattices. We investigate whether or not the Imry-Ma criterion, that predicts that random field disorder destroys phase transitions in equilibrium systems in sufficiently low dimensions, also holds for nonequilibrium phase transitions. We find that the Imry-Ma criterion does not apply to a prototypical absorbing state nonequilibrium transition.

In addition, we study the effect of disorder with long-range spatial correlations on the absorbing state phase transition in the contact process. Most importantly, we find that long-range correlations enhance the Griffiths singularities and change the universality class of the transition. We also investigate the absorbing state phase transition of the contact process with quasiperiodic transition rates using a real-space renormalization group which yields a complete theory of the resulting exotic infinite-modulation critical point.

Moreover, we study the effect of quenched disorder on a randomly layered Heisenberg magnet by means of a large-scale Monte-Carlo simulations. We find that the transition follows the infinite-randomness critical point scenario. Finally, we investigate the effect of quenched disorder on the first-order phase transition in the N-color quantum Ashkin-Teller model by means of strong-disorder renormalization group theory. We find that disorder rounds the first-order quantum phase transition in agreement with quantum version of the Imry-Ma criterion"--Abstract, page v.


Vojta, Thomas

Committee Member(s)

Wilemski, Gerald
Medvedeva, Julia E.
Parris, Paul Ernest, 1954-
Täuber, Uwe C.



Degree Name

Ph. D. in Physics


National Science Foundation (U.S.)


Missouri University of Science and Technology

Publication Date

Fall 2016

Journal article titles appearing in thesis/dissertation

  • Phase transitions on random lattices: How random is topological disorder?
  • Random fields at a nonequilibrium phase transition
  • Random field disorder at an absorbing state transition in one and two dimensions
  • Enhanced rare-region effects in the contact process with long-range correlated disorder
  • Contact process on generalized Fibonacci chains: Infinite-modulation criticality and double-log periodic oscillations
  • Infinite-randomness criticality in a randomly layered Heisenberg magnet
  • Strong-randomness phenomena in quantum Ashkin-Teller model


xx, 203 pages

Note about bibliography

Includes bibliographic references.


© Hatem Nuri Barghathi

Document Type

Dissertation - Open Access

File Type




Library of Congress Subject Headings

Phase transformations (Statistical physics)
Order-disorder models
Quantum theory -- Mathematical models
Nonequilibrium statistical mechanics
Lattice dynamics

Thesis Number

T 11012

Electronic OCLC #



This work has been supported in part by NSF under Grant Nos. DMR-0906566 and DMR-1205803 and PHYS-1066293, from Simons Foundation, from FAPESP under GrantNo. 2013/09850-7, and from CNPq under Grant Nos. 590093/2011-8 and 305261/2012-6.

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