Application of renormalization-group techniques to random magnetic systems
Jayaprakash, Ciriyam
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https://hdl.handle.net/2142/25563
Description
Title
Application of renormalization-group techniques to random magnetic systems
Author(s)
Jayaprakash, Ciriyam
Issue Date
1979
Doctoral Committee Chair(s)
Wortis, M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
renormalization-group techniques
random magnetic systems
quenched random magnetic systems
second-order phase transitions
momentum-space methods
position-space techniques
Language
en
Abstract
"Renorma1ization-group methods have been applied in the study of quenched
random magnetic systems in recent years. We begin with a brief review of
second-order phase transitions in pure, homogeneous systems and also of the .. renorma1ization group framework. Then we provide an introduction to quenched
random magnetic systems. Next, momentum-space methods and position-space
techniques as applied to quenched random magnets are outlined and compared.
Grinstein and Luther applied the Wilson-Fisher E-expansion to random
n-vector models; Khme1'nitsky discovered that the random Ising model (n = 1)
possessed a ""random"" fixed point of 0(squareroot(e)). This fixed point was found to
have one marginal and one irrelevant operator. We have investigated the
stability of this fixed point using Ca11an-Symanzik equations and renorma1ized
perturbation theory. We find the fixed point stable in the next order; we
have also obtained critical exponents to one higher order.
Next, position-space techniques are used to study some simple model
systems. In addition to critical exponents, global thermodynamic properties
are determined. These calculations are based on the Migda1-Kadanoff approximate
recursion relations suitably generalized to the inhomogeneous case.
Firstly we study the randomly bond-dilute two-dimensional nearest-
neighbor Ising model on a square lattice. Calculations give both thermal
and magnetic exponents associated with the percolative fixed point.
Differential recursion relations yield a phase diagram which is in quantitative agreement with all known results. Curves for the specific heat, percolation probability, and magnetization are displayed. The critical region of the specific heat becomes unobservably narrow well above the percolation threshold Pc. This provides a possible explanation for the apparent specific-heat rounding in certain experiments.
We then study the Edwards-Anderson model of a spin glass. The current theoretical situation, which is far from satisfactory at present, is briefly reviewed. We treat the spin-l/2 Ising model with independently random nearestneighbor interactions in dimensionalities d = 2, 3, and 4. The phase diagram, which is in qualitative agreement with mean-field results, exhibits paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass phases. The spinglass and paramagnetic phases meet along an extended second-order phase boundary, which terminates in two tricritical points. Critical and tricritical exponents are calculated. The spin-glass specific-heat exponent turns out to be large and negative, compatibly with recent experiments which show a rounded specific heat anomaly. Global specific-heat curves are also displayed for d = 2."
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