337 research outputs found
Random Fixed Point of Three-Dimensional Random-Bond Ising Models
The fixed-point structure of three-dimensional bond-disordered Ising models
is investigated using the numerical domain-wall renormalization-group method.
It is found that, in the +/-J Ising model, there exists a non-trivial fixed
point along the phase boundary between the paramagnetic and ferromagnetic
phases. The fixed-point Hamiltonian of the +/-J model numerically coincides
with that of the unfrustrated random Ising models, strongly suggesting that
both belong to the same universality class. Another fixed point corresponding
to the multicritical point is also found in the +/-J model. Critical properties
associated with the fixed point are qualitatively consistent with theoretical
predictions.Comment: 4 pages, 5 figures, to be published in Journal of the Physical
Society of Japa
Ordered phase and phase transitions in the three-dimensional generalized six-state clock model
We study the three-dimensional generalized six-state clock model at values of
the energy parameters, at which the system is considered to have the same
behavior as the stacked triangular antiferromagnetic Ising model and the
three-state antiferromagnetic Potts model. First, we investigate ordered phases
by using the Monte Carlo twist method (MCTM). We confirmed the existence of an
incompletely ordered phase (IOP1) at intermediate temperature, besides the
completely ordered phase (COP) at low-temperature. In this intermediate phase,
two neighboring states of the six-state model mix, while one of them is
selected in the low temperature phase. We examine the fluctuation the mixing
rate of the two states in IOP1 and clarify that the mixing rate is very stable
around 1:1.
The high temperature phase transition is investigated by using
non-equilibrium relaxation method (NERM). We estimate the critical exponents
beta=0.34(1) and nu=0.66(4). These values are consistent with the 3D-XY
universality class. The low temperature phase transition is found to be of
first-order by using MCTM and the finite-size-scaling analysis
On a Covariant Determination of Mass Scales in Warped Backgrounds
We propose a method of determining masses in brane scenarios which is
independent of coordinate transformations. We apply our method to the scenario
of Randall and Sundrum (RS) with two branes, which provides a solution to the
hierarchy problem. The core of our proposal is the use of covariant equations
and expressing all coordinate quantities in terms of invariant distances. In
the RS model we find that massive brane fields propagate proper distances
inversely proportional to masses that are not exponentially suppressed. The
hierarchy between the gravitational and weak interactions is nevertheless
preserved on the visible brane due to suppression of gravitational interactions
on that brane. The towers of Kaluza-Klein states for bulk fields are observed
to have different spacings on different branes when all masses are measured in
units of the fundamental scale. Ratios of masses on each brane are the same in
our covariant and the standard interpretations. Since masses of brane fields
are not exponentiated, the fundamental scale of higher-dimensional gravity must
be of the order of the weak scale.Comment: 14 page
The two-dimensional random-bond Ising model, free fermions and the network model
We develop a recently-proposed mapping of the two-dimensional Ising model
with random exchange (RBIM), via the transfer matrix, to a network model for a
disordered system of non-interacting fermions. The RBIM transforms in this way
to a localisation problem belonging to one of a set of non-standard symmetry
classes, known as class D; the transition between paramagnet and ferromagnet is
equivalent to a delocalisation transition between an insulator and a quantum
Hall conductor. We establish the mapping as an exact and efficient tool for
numerical analysis: using it, the computational effort required to study a
system of width is proportional to , and not exponential in as
with conventional algorithms. We show how the approach may be used to calculate
for the RBIM: the free energy; typical correlation lengths in quasi-one
dimension for both the spin and the disorder operators; even powers of
spin-spin correlation functions and their disorder-averages. We examine in
detail the square-lattice, nearest-neighbour RBIM, in which bonds are
independently antiferromagnetic with probability , and ferromagnetic with
probability . Studying temperatures , we obtain precise
coordinates in the plane for points on the phase boundary between
ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We
demonstrate scaling flow towards the pure Ising fixed point at small , and
determine critical exponents at the multicritical point.Comment: 20 pages, 25 figures, figures correcte
Critical behavior of the random-anisotropy model in the strong-anisotropy limit
We investigate the nature of the critical behavior of the random-anisotropy
Heisenberg model (RAM), which describes a magnetic system with random uniaxial
single-site anisotropy, such as some amorphous alloys of rare earths and
transition metals. In particular, we consider the strong-anisotropy limit
(SRAM), in which the Hamiltonian can be rewritten as the one of an Ising
spin-glass model with correlated bond disorder. We perform Monte Carlo
simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring
correlation functions of the replica-replica overlap, which is the order
parameter at a glass transition. The corresponding results show critical
behavior and finite-size scaling. They provide evidence of a finite-temperature
continuous transition with critical exponents and
. These results are close to the corresponding estimates that
have been obtained in the usual Ising spin-glass model with uncorrelated bond
disorder, suggesting that the two models belong to the same universality class.
We also determine the leading correction-to-scaling exponent finding .Comment: 24 pages, 13 figs, J. Stat. Mech. in pres
Disordered Systems and the Replica Method in AdS/CFT
We formulate a holographic description of effects of disorder in conformal
field theories based on the replica method and the AdS/CFT correspondence.
Starting with copies of conformal field theories, randomness with a
gaussian distribution is described by a deformation of double trace operators.
After computing physical quantities, we take the limit at the final
step. We compute correlation functions in the disordered systems by using the
holographic replica method as well as the formulation in the conformal field
theory. We find examples where disorder changes drastically the scaling of two
point functions. The renormalization group flow of the effective central charge
in our disordered systems is also discussed.Comment: 26 pages, references added, published versio
Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts
The XY model with quenched random disorder is studied by a zero temperature
domain wall renormalization group method in 2D and 3D. Instead of the usual
phase representation we use the charge (vortex) representation to compute the
domain wall, or defect, energy. For the gauge glass corresponding to the
maximum disorder we reconfirm earlier predictions that there is no ordered
phase in 2D but an ordered phase can exist in 3D at low temperature. However,
our simulations yield spin stiffness exponents in 2D
and in 3D, which are considerably larger than
previous estimates and strongly suggest that the lower critical dimension is
less than three. For the XY spin glass in 3D, we obtain a spin
stiffness exponent which supports the existence of
spin glass order at finite temperature in contrast with previous estimates
which obtain . Our method also allows us to study
renormalization group flows of both the coupling constant and the disorder
strength with length scale . Our results are consistent with recent analytic
and numerical studies suggesting the absence of a re-entrant transition in 2D
at low temperature. Some possible consequences and connections with real vortex
systems are discussed.Comment: 14 pages, 9 figures, revtex
Selective Molecular Sieving through Porous Graphene
Membranes act as selective barriers and play an important role in processes
such as cellular compartmentalization and industrial-scale chemical and gas
purification. The ideal membrane should be as thin as possible to maximize
flux, mechanically robust to prevent fracture, and have well-defined pore sizes
to increase selectivity. Graphene is an excellent starting point for developing
size selective membranes because of its atomic thickness, high mechanical
strength, relative inertness, and impermeability to all standard gases.
However, pores that can exclude larger molecules, but allow smaller molecules
to pass through have to be introduced into the material. Here we show
UV-induced oxidative etching can create pores in micrometre-sized graphene
membranes and the resulting membranes used as molecular sieves. A pressurized
blister test and mechanical resonance is used to measure the transport of a
variety of gases (H2, CO2, Ar, N2, CH4, and SF6) through the pores. The
experimentally measured leak rates, separation factors, and Raman spectrum
agree well with models based on effusion through a small number of
angstrom-sized pores.Comment: to appear in Nature Nanotechnolog
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