Scaling laws and correlation functions near magnetic critical points
Hecht, Robert Joseph
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/2142/25708
Description
Title
Scaling laws and correlation functions near magnetic critical points
Author(s)
Hecht, Robert Joseph
Issue Date
1967
Doctoral Committee Chair(s)
Kadanoff, L.P.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
scaling laws
correlation functions
magnetic critical points
Kadanoff's derivation
Language
en
Abstract
"Critical point phenomena in magnetic systems are studied
with the aid of the scaling laws. These laws relate the critical
indices which describe the behavior of thermodynamic and correlation
functions near T. Kadanoff's derivation of the scaling 1aw is
reviewed.
An experimental survey of ferromagnetic and antiferromagnetic
data near T is presented. Susceptibility, correlation length, magnectization, specific heat and a magnetic equation of state are discussed.
It is found that the ""critical region"" can extend as far as
[equation]
although frequently it is restricted to E < 10-2
The critical indices S, y, v, ~ and ~, are close to the three dimensional
ISing model values. Values for 0, y' and ~ are not
known as conclusively. Specific heat behavior is discussed in terms
-~ of a three-parameter fit, namely C = aE + b. Varying b allows one
to estimate a possible range of a's. The experimental information
is consistent with the scaling law relations 2 - alpha = 2 - alpha' = dV = d gamma / (2-pi) = gamma + 2B = B(d+1)
The scaling law theory is extended to predict the temperature,
field and spatial dependence of various spin correlation functions.
These predictions are checked by analytic calculations for the two dimensional
Ising model in zero field. Results are presented for the
energy density-energy density and energy density-spin correlation
functions in the limit E « 1, R » 1, but the product ER arbitrary.
Results are also presented for a group of two, three and four spin
correlations at cT. In each case the scaling law predictions are
verified."
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.
