Masters Theses


Mark Dickison


"This thesis focuses on the effects of both correlated and non-correlated disorder on non-equilibrium phase transitions, specifically those found in the d-dimensional contact process. These effects are studied by means of extensive Monte-Carlo simulations. The scaling behavior of various parameters is evaluated for both cases, and the results are compared with theory. For the correlated disorder case, the stationary density in the vicinity of the transition is also examined and found to be smeared.

The behavior in both cases can be understood as the results of rare regions where the system is locally free of disorder. For point-like defects, i.e., uncorrelated disorder, the rare regions are of finite size and cannot undergo a true phase transition. Instead, they fluctuate slowly which gives rise to Griffiths effects. In contrast, if the rare regions are infinite in at least one dimension, a stronger effect occurs: each rare region can independently undergo the phase transition and develop a nonzero steady state density. This leads to a smearing of the global transition"--Abstract, page iv.


Thomas Vojta

Committee Member(s)

Gerald Wilemski
David Grow



Degree Name

M.S. in Physics


University of Missouri--Rolla

Publication Date

Fall 2005

Journal article titles appearing in thesis/dissertation

  • Monte-Carlo simulations of the smeared phase transition in a contact process with extended defects


ix, 50 pages

Note about bibliography

includes bibliographical references (pages 48-49)


© 2005 Mark Dickison, All rights reserved.

Document Type

Thesis - Restricted Access

File Type




Subject Headings

Order-disorder models
Phase transformations (Statistical physics)
Condensed matter
Monte Carlo method

Thesis Number

T 8868

Print OCLC #


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