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Title:  Application of renormalizationgroup techniques to random magnetic systems 
Author(s):  Jayaprakash, Ciriyam 
Doctoral Committee Chair(s):  Wortis, M. 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  renormalizationgroup techniques
random magnetic systems quenched random magnetic systems secondorder phase transitions momentumspace methods positionspace techniques 
Abstract:  Renorma1izationgroup methods have been applied in the study of quenched random magnetic systems in recent years. We begin with a brief review of secondorder phase transitions in pure, homogeneous systems and also of the .. renorma1ization group framework. Then we provide an introduction to quenched random magnetic systems. Next, momentumspace methods and positionspace techniques as applied to quenched random magnets are outlined and compared. Grinstein and Luther applied the WilsonFisher Eexpansion to random nvector 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 Ca11anSymanzik 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, positionspace 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 Migda1Kadanoff approximate recursion relations suitably generalized to the inhomogeneous case. Firstly we study the randomly bonddilute twodimensional 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 specificheat rounding in certain experiments. We then study the EdwardsAnderson model of a spin glass. The current theoretical situation, which is far from satisfactory at present, is briefly reviewed. We treat the spinl/2 Ising model with independently random nearestneighbor interactions in dimensionalities d = 2, 3, and 4. The phase diagram, which is in qualitative agreement with meanfield results, exhibits paramagnetic, ferromagnetic, antiferromagnetic, and spinglass phases. The spinglass and paramagnetic phases meet along an extended secondorder phase boundary, which terminates in two tricritical points. Critical and tricritical exponents are calculated. The spinglass specificheat exponent turns out to be large and negative, compatibly with recent experiments which show a rounded specific heat anomaly. Global specificheat curves are also displayed for d = 2. 
Issue Date:  1979 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/25563 
Rights Information:  1979 Ciriyam Jayaprakash 
Date Available in IDEALS:  20110629 
Identifier in Online Catalog:  361040 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois