Breakdown of a conservation law in incommensurate systems

We show that invariance properties of the Lagrangian of an incommensurate system, as described by the Frenkel Kontorova model, imply the existence of a generalized angular momentum which is an integral of motion if the system remains floating. The behavior of this quantity can therefore monitor the character of the system as floating (when it is conserved) or locked (when it is not). We find that, during the dynamics, the non-linear couplings of our model cause parametric phonon excitations which lead to the appearance of Umklapp terms and to a sudden deviation of the generalized momentum from a constant value, signalling a dynamical transition from a floating to a pinned state. We point out that this transition is related but does not coincide with the onset of sliding friction which can take place when the system is still floating.Comment: 7 pages, 6 figures, typed with RevTex, submitted to Phys. Rev. E Replaced 27-03-2001: changes to text, minor revision of figure

Roughening Induced Deconstruction in (100) Facets of CsCl Type Crystals

The staggered 6-vertex model describes the competition between surface roughening and reconstruction in (100) facets of CsCl type crystals. Its phase diagram does not have the expected generic structure, due to the presence of a fully-packed loop-gas line. We prove that the reconstruction and roughening transitions cannot cross nor merge with this loop-gas line if these degrees of freedom interact weakly. However, our numerical finite size scaling analysis shows that the two critical lines merge along the loop-gas line, with strong coupling scaling properties. The central charge is much larger than 1.5 and roughening takes place at a surface roughness much larger than the conventional universal value. It seems that additional fluctuations become critical simultaneously.Comment: 31 pages, 9 figure

Monte Carlo simulation of ice models

We propose a number of Monte Carlo algorithms for the simulation of ice models and compare their efficiency. One of them, a cluster algorithm for the equivalent three colour model, appears to have a dynamic exponent close to zero, making it particularly useful for simulations of critical ice models. We have performed extensive simulations using our algorithms to determine a number of critical exponents for the square ice and F models.Comment: 32 pages including 15 postscript figures, typeset in LaTeX2e using the Elsevier macro package elsart.cl

Equilibrium shapes and faceting for ionic crystals of body-centered-cubic type

A mean field theory is developed for the calculation of the surface free energy of the staggered BCSOS, (or six vertex) model as function of the surface orientation and of temperature. The model approximately describes surfaces of crystals with nearest neighbor attractions and next nearest neighbor repulsions. The mean field free energy is calculated by expressing the model in terms of interacting directed walks on a lattice. The resulting equilibrium shape is very rich with facet boundaries and boundaries between reconstructed and unreconstructed regions which can be either sharp (first order) or smooth (continuous). In addition there are tricritical points where a smooth boundary changes into a sharp one and triple points where three sharp boundaries meet. Finally our numerical results strongly suggest the existence of conical points, at which tangent planes of a finite range of orientations all intersect each other. The thermal evolution of the equilibrium shape in this model shows strong similarity to that seen experimentally for ionic crystals.Comment: 14 Pages, Revtex and 10 PostScript figures include

Correlated percolation and the correlated resistor network

We present some exact results on percolation properties of the Ising model, when the range of the percolating bonds is larger than nearest-neighbors. We show that for a percolation range to next-nearest neighbors the percolation threshold Tp is still equal to the Ising critical temperature Tc, and present the phase diagram for this type of percolation. In addition, we present Monte Carlo calculations of the finite size behavior of the correlated resistor network defined on the Ising model. The thermal exponent t of the conductivity that follows from it is found to be t = 0.2000 +- 0.0007. We observe no corrections to scaling in its finite size behavior.Comment: 16 pages, REVTeX, 6 figures include

Finite-size scaling and conformal anomaly of the Ising model in curved space

We study the finite-size scaling of the free energy of the Ising model on lattices with the topology of the tetrahedron and the octahedron. Our construction allows to perform changes in the length scale of the model without altering the distribution of the curvature in the space. We show that the subleading contribution to the free energy follows a logarithmic dependence, in agreement with the conformal field theory prediction. The conformal anomaly is given by the sum of the contributions computed at each of the conical singularities of the space, except when perfect order of the spins is precluded by frustration in the model.Comment: 4 pages, 4 Postscript figure

Dynamic Critical Behavior of a Swendsen-Wang-Type Algorithm for the Ashkin-Teller Model

We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin--Teller model. We find that the Li--Sokal bound on the autocorrelation time ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$) holds along the self-dual curve of the symmetric Ashkin--Teller model, and is almost but not quite sharp. The ratio $\tau_{{\rm int},{\cal E}} / C_H$ appears to tend to infinity either as a logarithm or as a small power ($0.05 \leq p \leq 0.12$). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.Comment: 59 pages including 3 figures, uuencoded g-compressed ps file. Postscript size = 799740 byte

Berry phase and adiabaticity of a spin diffusing in a non-uniform magnetic field

An electron spin moving adiabatically in a strong, spatially non-uniform magnetic field accumulates a geometric phase or Berry phase, which might be observable as a conductance oscillation in a mesoscopic ring. Two contradicting theories exist for how strong the magnetic field should be to ensure adiabaticity if the motion is diffusive. To resolve this controversy, we study the effect of a non-uniform magnetic field on the spin polarization and on the weak-localization effect. The diffusion equation for the Cooperon is solved exactly. Adiabaticity requires that the spin-precession time is short compared to the elastic scattering time - it is not sufficient that it is short compared to the diffusion time around the ring. This strong condition severely complicates the experimental observation.Comment: 16 pages REVTEX, including 3 figure

Evidence for Complex Subleading Exponents from the High-Temperature Expansion of the Hierarchical Ising Model

Using a renormalization group method, we calculate 800 high-temperature coefficients of the magnetic susceptibility of the hierarchical Ising model. The conventional quantities obtained from differences of ratios of coefficients show unexpected smooth oscillations with a period growing logarithmically and can be fitted assuming corrections to the scaling laws with complex exponents.Comment: 10 pages, Latex , uses revtex. 2 figures not included (hard copies available on request

Dynamics of Particles Deposition on a Disordered Substrate: II. Far-from Equilibrium Behavior. -

The deposition dynamics of particles (or the growth of a rigid crystal) on a disordered substrate at a finite deposition rate is explored. We begin with an equation of motion which includes, in addition to the disorder, the periodic potential due to the discrete size of the particles (or to the lattice structure of the crystal) as well as the term introduced by Kardar, Parisi, and Zhang (KPZ) to account for the lateral growth at a finite growth rate. A generating functional for the correlation and response functions of this process is derived using the approach of Martin, Sigga, and Rose. A consistent renormalized perturbation expansion to first order in the non-Gaussian couplings requires the calculation of diagrams up to three loops. To this order we show, for the first time for this class of models which violates the the fluctuation-dissipation theorem, that the theory is renormalizable. We find that the effects of the periodic potential and the disorder decay on very large scales and asymptotically the KPZ term dominates the behavior. However, strong non-trivial crossover effects are found for large intermediate scales.Comment: 52 pages & 17 Figs in uucompressed file. UR-CM 94-090