Roughening and preroughening transitions in crystal surfaces with double-height steps

We investigate phase transitions in a solid-on-solid model where double-height steps as well as single-height steps are allowed. Without the double-height steps, repulsive interactions between up-up or down-down step pairs give rise to a disordered flat phase. When the double-height steps are allowed, two single-height steps can merge into a double-height step (step doubling). We find that the step doubling reduces repulsive interaction strength between single-height steps and that the disordered flat phase is suppressed. As a control parameter a step doubling energy is introduced, which is assigned to each step doubling vertex. From transfer matrix type finite-size-scaling studies of interface free energies, we obtain the phase diagram in the parameter space of the step energy, the interaction energy, and the step doubling energy.Comment: 4 pages, 5 figure

ENVIRONMENTAL POLICY ISSUES: CHAOS AND CONFUSION

Environmental Economics and Policy,

Cosmological perturbations in a generalized gravity including tachyonic condensation

We present unified ways of handling the cosmological perturbations in a class of gravity theory covered by a general action in eq. (1). This gravity includes our previous generalized $f(\phi,R)$ gravity and the gravity theory motivated by the tachyonic condensation. We present general prescription to derive the power spectra generated from vacuum quantum fluctuations in the slow-roll inflation era. An application is made to a slow-roll inflation based on the tachyonic condensation with an exponential potential.Comment: 5 page

Interacting Domain Walls and the Five-Vertex Model

We investigate the thermodynamic and critical properties of an interacting domain wall model which is derived from the triangular lattice antiferromagnetic Ising model with the anisotropic nearest and next nearest neighbor interactions. The model is equivalent to the general five--vertex model. Diagonalizing the transfer matrix exactly by the Bethe Ansatz method, we obtain the phase diagram displaying the commensurate and incommensurate (IC) phases separated by the Pokrovsky--Talapov transitions. The phase diagram exhibits commensurate phases where the domain wall density $q$ is locked at the values of $0$, $1/2$ and $1$. The IC phase is a critical state described by the Gaussian fixed point. The effective Gaussian coupling constant is obtained analytically and numerically for the IC phase using the finite size scaling predictions of the conformal field theory. It takes the value $1/2$ in the non-interacting limit and also at the boundaries of $q=0$ or $1$ phase and the value $2$ at the boundary of $q=1/2$ phase, while it varies smoothly throughout the IC region. (TO APPEAR IN PHY. REV. E)Comment: 43 pages +12 figures on request, REVTEX, SNUTP-93-6

Second-order Perturbations of the Friedmann World Model

We consider instability of the Friedmann world model to the second-order in perturbations. We present the perturbed set of equations up to the second-order in the Friedmann background world model with general spatial curvature and the cosmological constant. We consider systems with the completely general imperfect fluids, the minimally coupled scalar fields, the electro-magnetic field, and the generalized gravity theories. We also present the case of null geodesic equations, and the one based on the relativistic Boltzmann equation. In due stage a decomposition is made for the scalar-, vector- and tensor-type perturbations which couple each other to the second-order. Gauge issue is resolved to each order. The basic equations are presented without imposing any gauge condition, thus in a gauge-ready form so that we can use the full advantage of having the gauge freedom in analysing the problems. As an application we show that to the second-order in perturbation the relativistic pressureless ideal fluid of the scalar-type reproduces exactly the known Newtonian result. As another application we rederive the large-scale conserved quantities (of the pure scalar- and tensor-perturbations) to the second order, first shown by Salopek and Bond, now from the exact equations. Several other applications are made as well.Comment: 61 pages; published version in Phys. Rev.