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The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.
The production of topological defects, especially cosmic strings, in extended inflation models was considered. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large scale structure via cosmic strings.
We examine the dynamics of the electroweak phase transition in the early Universe. For Higgs masses in the range 46 less than or = M sub H less than or = 150 GeV and top quark masses less than 200 GeV, regions of symmetric and asymmetric vacuum coexist to below the critical temperature, with thermal equilibrium between the two phases maintained by fluctuations of both phases. We propose that the transition to the asymmetric vacuum is completed by percolation of these subcritical fluctuations. Our results are relevant to scenarios of baryogenesis that invoke a weakly first-order phase transition at the electroweak scale.
We examine the dynamics of the electroweak phase transition in the early Universe. For Higgs masses in the range 46 less than or = M sub H less than or = 150 GeV and top quark masses less than 200 GeV, regions of symmetric and asymmetric vacuum coexist to below the critical temperature, with thermal equilibrium between the two phases maintained by fluctuations of both phases. We propose that the transition to the asymmetric vacuum is completed by percolation of these subcritical fluctuations. Our results are relevant to scenarios of baryogenesis that invoke a weakly first-order phase transition at the electroweak scale.
In extended inflation, the inflationary era is brought to a close by the process of percolation of true vacuum bubbles produced in a first-order phase transition. This paper discusses several effects that might obtain if the universe undergoes an inflationary first-order phase transition.
I discuss the most recent model of inflation. In first-order inflation the inflationary epoch is associated with a first-order phase transition, with the most likely candidate being GUT symmetry breaking. The transition from the false-vacuum inflationary phase to the true-vacuum radiation-dominated phase proceeds through the nucleation and percolation of true-vacuum bubbles. The first successful and simplest model of first-order inflation, extended inflation, is discussed in some detail: evolution of the cosmic-scale factor, reheating, density perturbations, and the production of gravitational waves both from quantum fluctuations and bubble collisions. Particular attention is paid to the most critical issue in any model of first-order inflation: the requirements on the nucleation rate to ensure a graceful transition from the inflationary phase to the radiation-dominated phase.
In extended inflation, a new version of inflation where the transition from the false-vacuum phase to a radiation-dominated Universe is accomplished by bubble nucleation and percolation, bubble collisions supply a potent-and potentially detectable-source of gravitational waves. The present energy density in relic gravity waves from bubble collisions is expected to be about 10(exp -5) of closure density-many orders of magnitude greater than that of the gravity waves produced by quantum fluctuations. Their characteristic wavelength depends upon the reheating temperature T(sub RH): lambda is approximately 10(exp 4) cm (10(exp 14) GeV/T(sub RH)). If large numbers of black holes are produced, a not implausible outcome, they will evaporate producing comparable amounts of shorter wavelength waves, lambda is approximately 10(exp -6) cm (T(sub RH)/10(exp 14) GeV).
The viscosity of the three-component microemulsion water/decane/AOT has been measured as a function of temperature and droplet volume fraction. At temperatures well below the phase-separation temperature the viscosity is described by treating the droplets as hard spheres suspended in decane. Upon approaching the two-phase region from low temperature, there is a large (as much as a factor of four) smooth increase of the viscosity which may be related to the percolation-like transition observed in the electrical conductivity. This increase in viscosity is not completely consistent with either a naive electroviscous model or a simple clustering model. The divergence of the viscosity near the critical point (39 C) is superimposed upon the smooth increase. The magnitude and temperature dependence of the critical divergence are similar to that seen near the critical points of binary liquid mixtures.