Energy density correlations in the three-dimensional Ising model
Rutherford, Reginald
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/30673
Description
Title
Energy density correlations in the three-dimensional Ising model
Author(s)
Rutherford, Reginald
Issue Date
1973
Director of Research (if dissertation) or Advisor (if thesis)
M. Wortis
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
energy density correlation function
Ising model
phase transitions
face-centered cubic lattice
Language
en
Abstract
The energy-density-energy-density correlation function is studied in the three-dimensional Ising model in zero external field, for various spins on the fcc lattice. An extension of the linked-cluster technique is used to obtain high-temperature series expansions for the correlation function and its associated functions, to at least eighth order in the high-temperature interaction variable. Analysis of the series provides values for their critical indices and amplitudes. These values are used to verify the predictions of several theories of critical behavior.
The critical index of the coherence length of the energy density correlation function is found to be equal to that of the spin-spin correlation function for all spins within the accuracy obtained here. For spins higher than ~ this critical index appears to obey strong scaling.
An analysis of universality indicates that only one scale factor is needed to transform the energy density correlation function from one spin to another. This prediction is checked here and found to be good within our present accuracy.
The current-algebra hypothesis predicts definite relations between the leading singularities of various correlation functions at the critical point. This prediction is checked directly and consistent values of the leading coefficients are obtained.
The shape of the energy density correlation function at large distances from the origin, both at and above the critical point, is determined. The results are sufficiently accurate to rule out the Ornstein-Zernike form
in zero field for T > T , but not sufficient to eliminate the possibility
c of anisotropy at T = T .
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
