25 research outputs found
The "Coulomb phase" in frustrated systems
The "Coulomb phase" is an emergent state for lattice models (particularly
highly frustrated antiferromagnets) which have local constraints that can be
mapped to a divergence-free "flux". The coarse-grained version of this flux or
polarization behave analogously to electric or magnetic fields; in particular,
defects at which the local constraint is violated behave as effective charges
with Coulomb interactions. I survey the derivation of the characteristic
power-law correlation functions and the pinch-points in reciprocal space plots
of diffuse scattering, as well as applications to magnetic relaxation,
quantum-mechanical generalizations, phase transitions to long-range-ordered
states, and the effects of disorder.Comment: 30 pp, 5 figures (Sub. to Annual Reviews of Condensed Matter Physics
Nishimori point in random-bond Ising and Potts models in 2D
We study the universality class of the fixed points of the 2D random bond
q-state Potts model by means of numerical transfer matrix methods. In
particular, we determine the critical exponents associated with the fixed point
on the Nishimori line. Precise measurements show that the universality class of
this fixed point is inconsistent with percolation on Potts clusters for q=2,
corresponding to the Ising model, and q=3Comment: 11 pages, 3 figures. Contribution to the proceedings of the NATO
Advanced Research Workshop on Statistical Field Theories, Como 18-23 June
200
Criticality in correlated quantum matter
At quantum critical points (QCP)
\cite{Pfeuty:1971,Young:1975,Hertz:1976,Chakravarty:1989,Millis:1993,Chubukov:1
994,Coleman:2005} there are quantum fluctuations on all length scales, from
microscopic to macroscopic lengths, which, remarkably, can be observed at
finite temperatures, the regime to which all experiments are necessarily
confined. A fundamental question is how high in temperature can the effects of
quantum criticality persist? That is, can physical observables be described in
terms of universal scaling functions originating from the QCPs? Here we answer
these questions by examining exact solutions of models of correlated systems
and find that the temperature can be surprisingly high. As a powerful
illustration of quantum criticality, we predict that the zero temperature
superfluid density, , and the transition temperature, , of
the cuprates are related by , where the exponent
is different at the two edges of the superconducting dome, signifying the
respective QCPs. This relationship can be tested in high quality crystals.Comment: Final accepted version not including minor stylistic correction
Programmable disorder in random DNA tilings
Scaling up the complexity and diversity of synthetic molecular structures will require strategies that exploit the inherent stochasticity of molecular systems in a controlled fashion. Here we demonstrate a framework for programming random DNA tilings and show how to control the properties of global patterns through simple, local rules. We constructed three general forms of planar network—random loops, mazes and trees—on the surface of self-assembled DNA origami arrays on the micrometre scale with nanometre resolution. Using simple molecular building blocks and robust experimental conditions, we demonstrate control of a wide range of properties of the random networks, including the branching rules, the growth directions, the proximity between adjacent networks and the size distribution. Much as combinatorial approaches for generating random one-dimensional chains of polymers have been used to revolutionize chemical synthesis and the selection of functional nucleic acids, our strategy extends these principles to random two-dimensional networks of molecules and creates new opportunities for fabricating more complex molecular devices that are organized by DNA nanostructures
Conjectures on exact solution of three - dimensional (3D) simple orthorhombic Ising lattices
We report the conjectures on the three-dimensional (3D) Ising model on simple
orthorhombic lattices, together with the details of calculations for a putative
exact solution. Two conjectures, an additional rotation in the fourth curled-up
dimension and the weight factors on the eigenvectors, are proposed to serve as
a boundary condition to deal with the topologic problem of the 3D Ising model.
The partition function of the 3D simple orthorhombic Ising model is evaluated
by spinor analysis, by employing these conjectures. Based on the validity of
the conjectures, the critical temperature of the simple orthorhombic Ising
lattices could be determined by the relation of KK* = KK' + KK'' + K'K'' or
sinh 2K sinh 2(K' + K'' + K'K''/K) = 1. For a simple cubic Ising lattice, the
critical point is putatively determined to locate exactly at the golden ratio
xc = exp(-2Kc) = (sq(5) - 1)/2, as derived from K* = 3K or sinh 2K sinh 6K = 1.
If the conjectures would be true, the specific heat of the simple orthorhombic
Ising system would show a logarithmic singularity at the critical point of the
phase transition. The spontaneous magnetization and the spin correlation
functions of the simple orthorhombic Ising ferromagnet are derived explicitly.
The putative critical exponents derived explicitly for the simple orthorhombic
Ising lattices are alpha = 0, beta = 3/8, gamma = 5/4, delta = 13/3, eta = 1/8
and nu = 2/3, showing the universality behavior and satisfying the scaling
laws. The cooperative phenomena near the critical point are studied and the
results obtained based on the conjectures are compared with those of the
approximation methods and the experimental findings. The 3D to 2D crossover
phenomenon differs with the 2D to 1D crossover phenomenon and there is a
gradual crossover of the exponents from the 3D values to the 2D ones.Comment: 176 pages, 4 figure