High-temperature critical indices for the classical anisotropic Heisenberg model
Jasnow, David Michael
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https://hdl.handle.net/2142/25760
Description
Title
High-temperature critical indices for the classical anisotropic Heisenberg model
Author(s)
Jasnow, David Michael
Issue Date
1969
Doctoral Committee Chair(s)
Wortis, M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
high-temperature critical indices
classical anisotropic Heisenberg model
spin-spin correlation
Language
en
Abstract
The classical anisotropic Heisenberg model is studied
by means of high-temperature expansions. The purpose of the work
is to determine (in the context of the model) how many phase transitions
(as characterized by the critical exponents) there are, and
which features of the dynamics and kinematics of a given system
determine the dritical exponents.
A diagrammatic expansion for the Slpin-spin correlation
function is derived and renormalized. The resulting form of the
perturbation theory has been used to derive high-temperature series,
for various lattices and anisotropies, through orderT (closepacked
lattices) and T- 9 (loose-packed lattices). These series for
the correlation functions are combined to form series for the zerofield
susceptibility, second moment of correlations, and specific
heat.
The methods used to extract the critcal indices y (susceptibility),
V (correlation range) and alpha (specific heat) from the
series coefficients are discussed in detail. The results areconsistent
with the. hypothesis that the critical indices only change when
there is a change in the symmetry of the system, e.g. in interpolating
between the Ising and isotropic Heisenberg models, indices remain
Ising-like until the system is isotropic, at which point they
appear to change discontinuously.
The classical anisotropic planar Heisenberg model is
also studied. The possibility of the isotropic limit being a
lattice model of the A-transition of liquid He4 is discussed. The
results for the 'model are compared with experiment.
In view of recent interest in spinel structures and to
present a graphic example of the dangers which lie in attempts to
extrapolate too-short series, some results for that lattice are
given.
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