University of Illinois Urbana-Champaign

Theory of the two-dimensional Ising model with random impurities

Palciauskas, Vytautas Victor

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https://hdl.handle.net/2142/16596

Description

Title
Theory of the two-dimensional Ising model with random impurities
Author(s)
Palciauskas, Vytautas Victor
Issue Date
1969
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
two-dimensional ising model
Language
en
Abstract
The effects of random impurities on the various thermodynamic functions are studied with the aid of the two-dimensional Ising model. Of special interest are the limiting forms of these functions near the critical point. This problem is approached by a Green's function formulation as developed by Kadanoff. Since experiments only measure the average effects of impurities, we consider the average of the Green's function over all distributions of impurities and calculate it by perturbation theory. From this function we find the location of the new critical temperature and the temperature dependence of the coherence length. Thermodynamic and correlation functions are calculated by means of perturbation expansions and their functional dependence on the coherence length investigated. It is found that the magnetic properties such as the magnetization, susceptibility, and spin-spin correlations retain the same functional dependence on the coherence length. The specific heat is found to have a finite value at the critical point, and the T = Tc form of the energy-energy correlation c function is changed. The thermodynamic functions exhibit new critical indices very close to Tc. These renormalized exponents have been predicted c in literature and are found to satisfy the scaling laws predictions.
Type of Resource
text
Permalink
http://hdl.handle.net/2142/16596
Copyright and License Information
© 1969 Vytautas Victor Palciauskas

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