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Syracuse University

Condensed Matter

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Full-Text Articles in Physics

Topology Of Smectic Order On Compact Substrates, Xiangiun Xing Jan 2007

Topology Of Smectic Order On Compact Substrates, Xiangiun Xing

Physics

Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on torus as well as on sphere, we find that both systems exhibit many topologically distinct low energy states, that can be characterized by two integer topological charges. The total number of low energy states scales as the square root of the substrate area ...


Numerical Results For The Ground-State Interface In A Random Medium, Alan Middleton Jan 1995

Numerical Results For The Ground-State Interface In A Random Medium, Alan Middleton

Physics

The problem of determining the ground state of a $d$-dimensional interface embedded in a $(d+1)$-dimensional random medium is treated numerically. Using a minimum-cut algorithm, the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow. In particular, results are presented for the roughness exponents and ground-state energy fluctuations in a random bond Ising model. It is found that the roughness exponent $\zeta = 0.41 \pm 0.01, 0.22 \pm 0.01$, with the related energy exponent being $\theta = 0.84 \pm 0.03, 1.45 \pm ...


Translational Correlations In The Vortex Array At The Surface Of A Type-Ii Superconductor, M. Cristina Marchetti, David R. Nelson Jan 1992

Translational Correlations In The Vortex Array At The Surface Of A Type-Ii Superconductor, M. Cristina Marchetti, David R. Nelson

Physics

We discuss the statistical mechanics of magnetic flux lines in a finite-thickness slab of type-II superconductor. The long wavelength properties of a flux-line liquid in a slab geometry are described by a hydrodynamic free energy that incorporates the boundary conditions on the flux lines at the sample's surface as a surface contribution to the free energy. Bulk and surface weak disorder are modeled via Gaussian impurity potentials. This free energy is used to evaluate the two-dimensional structure factor of the flux-line tips at the sample surface. We find that surface interaction always dominates in determining the decay of translational ...