The high-order behavior of the perturbation expansion in the cubic replica field theory of spin glasses in the paramagnetic phase has been investigated. The study starts with the zero-dimensional version of the replica field theory and this is shown to be equivalent to the problem of finding finite size corrections in a modified spherical spin glass near the critical temperature. We find that the highorder behavior of the perturbation series is described, to leading order, by coefficients of alternating signs (suggesting that the cubic field theory is well-defined) but that there are also subdominant terms with a complicated dependence of their sign on the order. Our results are then extended to the d-dimensional field theory and in particular used to determine the high-order behavior of the terms in the expansion of the critical exponents in a power series in ǫ = 6 − d. We have also corrected errors in the existing ǫ expansions at third order.

Homogeneous and heterogeneous nucleations in a reduced-dimensional system undergoing a firstorder structural phase transition were examined by using low electron energy diffraction and scanning tunneling microscopy. The high-temperature 4 × 1 phase of a Si(111)-In surface was supercooled at temperatures below the transition temperature (T c ) and evolved slowly into a low-temperature 8 × 2 phase with time. The transition rate decreased significantly as the temperature approached T c . The kinetics of the observed homogeneous nucleation was analyzed by classical nucleation theory. The introduction of oxygen atoms reduced the hysteresis and accelerated nucleation significantly, showing that the T c -raising oxygen impurity plays the role of a nucleation seed for heterogeneous nucleation.

The structural phase transition of an In/Si(111) surface was examined by low-energy electron diffraction (LEED). The transition temperature between the room-temperature 4×1 structure and low-temperature 8×2 structure was determined from the changes in the LEED intensity of the half-order (×2), eighth-order (8×), and fourth-order (4×) spots with temperature. The transition temperatures determined independently from three sets of LEED beam spots were within 1 K. The differently prepared In/Si(111)−4×1 surfaces, which had similar LEED quality at room temperature, showed variations of the transition temperature. The differences in the measured transition temperatures were attributed to the effects of the additional In adatoms remaining on the surface during the formation of a 4×1 reconstruction. The In adatoms suppress the condensation of the (8×2) phase, decreasing the phase transition temperature and rounding the otherwise sharp transition.

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