Phase Transitions in Disordered Systems: I. Exciton/electron-Hole Liquid/plasma System in Germanium and Ii. Amorphous Ferromagnets and Spin Glasses

212 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981.In Part I of this thesis, we present experimental evidence demonstrating that a metal-insulator (M-I) phase transition can occur separately from the liquid-gas (L-G) transition in the exciton/electron-hole (e-h) gas/e-h liquid system in stressed Ge. Using a strain well to confine the photoexcited carriers, we analyzed the spectral content and spatial distribution of e-h recombination luminescence. We observe a line of first-order transitions between the exciton gas and e-h gas occurring up to 7 K which we associate with the M-I transition. This is well above the temperature of the L-G critical point which we found to be 4.5 (+OR-) 0.5 K with a critical density of 3 (+OR-) 1 x 10('16) cm. Spectroscopic evidence is also presented for a triple point which we estimate to be about 4 K. At this temperature, we were able to fit our measured luminescence spectra at particular photoexcitation powers only by including a theoretical line shape for the e-h gas with a density of 2.0 (+OR-) .5 x 10('16) cm('-3). A simple expansion of the free energy of the e-h system is presented from which we calculate a critical temperature for the M-I transition of 5.4 K which, possible because of quantum effects, is substantially below our measured value. Lifetime measurements of the different phases of the e-h system are also made. In particular, we have measured an extremely long lifetime of 1.5 ms for strain-confined excitons below 3.2 K. This compares favorably with our predicted radiative lifetime of 2.0 ms in stressed Ge. Above 3.2 K, a rapid decrease in the exciton lifetime is observed with increasing temperature, concurrent with an exponential decrease in the observed luminescence intensity. Three models for thermally-activated loss of strain-confined excitons are considered as possible explanations.In Part II of this thesis, we obtain the thermodynamic properties of a system of Ising spins interacting with various random potentials in the Bethe-Peierls-Weiss (BPW) approximation. When the effective number of neighbors z approaches infinity, we show that all the magnetic properties arising from a BPW approximation, the mean-random-field (MRF) and the Sherrington-Kirkpatrick (SK) replica treatment are identical. Also, the microscopic internal energy in the BPW method can be integrated appropriately to obtain a microscopic free energy which is identical to that derived by diagrammatic expansions of the disordered Hamiltonian. Using this free energy and our calculated distribution of internal fields, we show that the BPW method reproduces all the results of SK including a negative entropy of -k/(2(pi)) at T = 0. We also show by analytical means that a square hole or gap arises in the low-temperature distribution of the single-particle excitation fields h(,0) at h(,0) = 0 in the limit of infinite z. In an externally applied field, the hole remains centered about the zero value of the total (internal plus external) field. The reasons for the unphysical low-temperature results occurring in both the SK and BPW treatments are clarified in our discussion of this gap. The phase diagram as a function of z is calculated within the MRF approximation. We find that for z > 8 the phase diagram is already very close to that of the infinite z case. Finally, we compare magnetization versus temperature curves which have been calculated within Handrich's approach with those calculated within the BPW approach in the limit of infinite z. The two approximations are very similar for small amounts of disorder but Handrich's method breaks down as the amount of disorder approaches the spin-glas boundary.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD