1,653 research outputs found
Phase transitions in the one-dimensional frustrated quantum XY model and Josephson-junction ladders
A one-dimensional quantum version of the frustrated XY (planar rotor) model
is considered which can be physically realized as a ladder of
Josephson-junctions at half a flux quantum per plaquette. This system undergoes
a superconductor to insulator transition at zero temperature as a function of
charging energy. The critical behavior is studied using a Monte Carlo transfer
matrix applied to the path-integral representation of the model and a
finite-size-scaling analysis of data on small system sizes. Depending on the
ratio between the interchain and intrachain couplings the system can have
single or double transitions which is consistent with the prediction that its
critical behavior should be described by the two-dimensional classical XY-Ising
model.Comment: 13 pages, Revtex, J. Appl. Phys. (to appear), Inpe-las-00
Conformal Anomaly and Critical Exponents of the XY-Ising Model
We use extensive Monte Carlo transfer matrix calculations on infinite strips
of widths up to 30 lattice spacing and a finite-size scaling analysis to
obtain critical exponents and conformal anomaly number for the
two-dimensional -Ising model. This model is expected to describe the
critical behavior of a class of systems with simultaneous and
symmetries of which the fully frustrated model is a special case. The
effective values obtained for show a significant decrease with at
different points along the line where the transition to the ordered phase takes
place in a single transition. Extrapolations based on power-law corrections
give values consistent with although larger values can not be ruled
out. Critical exponents are obtained more accurately and are consistent with
previous Monte Carlo simulations suggesting new critical behavior and with
recent calculations for the frustrated model.Comment: 33 pages, 13 latex figures, uses RevTeX 3.
Decoupling in the 1D frustrated quantum XY model and Josephson junction ladders: Ising critical behavior
A generalization of the one-dimensional frustrated quantum XY model is
considered in which the inter and intra-chain coupling constants of the two
infinite XY (planar rotor) chains have different strengths. The model can
describe the superconductor to insulator transition due to charging effects in
a ladder of Josephson junctions in a magnetic field with half a flux quantum
per plaquette. From a fluctuation-effective action, this transition is expected
to be in the universality class of the two-dimensional classical XY-Ising
model. The critical behavior is studied using a Monte Carlo transfer matrix
applied to the path-integral representation of the model and a
finite-size-scaling analysis of data on small system sizes. It is found that,
unlike the previous studied case of equal inter and intra-chain coupling
constants, the XY and Ising-like excitations of the quantum model decouple for
large interchain coupling, giving rise to pure Ising model critical behavior
for the chirality order parameter and a superconductor-insulator transition in
the universality class of the 2D classical XY model.Comment: 15 pages with figures, RevTex 3.0, INPE-93/00
Zero-temperature resistive transition in Josephson-junction arrays at irrational frustration
We use a driven Monte Carlo dynamics in the phase representation to determine
the linear resistivity and current-voltage scaling of a two-dimensional
Josephson-junction array at an irrational flux quantum per plaquette. The
results are consistent with a phase-coherence transition scenario where the
critical temperature vanishes. The linear resistivity is nonzero at any finite
temperatures but nonlinear behavior sets in at a temperature-dependent
crossover current determined by the thermal critical exponent. From a dynamic
scaling analysis we determine this critical exponent and the thermally
activated behavior of the linear resistivity. The results are in agreement with
earlier calculations using the resistively shunted-junction model for the
dynamics of the array. The linear resistivity behavior is consistent with some
experimental results on arrays of superconducting grains but not on wire
networks, which we argue have been obtained in a current regime above the
crossover current.Comment: 7 pages, 5 figures, to appear in Phys. Rev.
Phase transitions in a frustrated XY model with zig-zag couplings
We study a new generalized version of the square-lattice frustrated XY model
where unequal ferromagnetic and antiferromagnetic couplings are arranged in a
zig-zag pattern. The ratio between the couplings can be used to tune the
system, continuously, from the isotropic square-lattice to the
triangular-lattice frustrated XY model. The model can be physically realized as
a Josephson-junction array with two different couplings, in a magnetic field
corresponding to half-flux quanta per plaquette. Mean-field approximation,
Ginzburg-Landau expansion and finite-size scaling of Monte Carlo simulations
are used to study the phase diagram and critical behavior. Depending on the
value of , two separate transitions or a transition line in the
universality class of the XY-Ising model, with combined and U(1)
symmetries, takes place. In particular, the phase transitions of the standard
square-lattice and triangular-lattice frustrated XY models correspond to two
different cuts through the same transition line. Estimates of the chiral
() critical exponents on this transition line deviate significantly from
the pure Ising values, consistent with that along the critical line of the
XY-Ising model. This suggests that a frustrated XY model or Josephson-junction
array with a zig-zag coupling modulation can provide a physical realization of
the XY-Ising model critical line.Comment: 11 pages, 9 figures, RevTex, to appear in Phys. Rev.
Phase-coherence threshold and vortex-glass state in diluted Josephson-junction arrays in a magnetic field
We study numerically the interplay of phase coherence and vortex-glass state
in two-dimensional Josephson-junction arrays with average rational values of
flux quantum per plaquette and random dilution of junctions. For ,
we find evidence of a phase coherence threshold value , below the
percolation concentration of diluted junctions , where the superconducting
transition vanishes. For the array behaves as a
zero-temperature vortex glass with nonzero linear resistance at finite
temperatures. The zero-temperature critical currents are insensitive to
variations in in the vortex glass region while they are strongly
dependent in the phase coherent region.Comment: 6 pages, 4 figures, to appear in Phys. Rev.
Numerical Studies of the Two Dimensional XY Model with Symmetry Breaking Fields
We present results of numerical studies of the two dimensional XY model with
four and eight fold symmetry breaking fields. This model has recently been
shown to describe hydrogen induced reconstruction on the W(100) surface. Based
on mean-field and renormalization group arguments,we first show how the
interplay between the anisotropy fields can give rise to different phase
transitions in the model. When the fields are compatible with each other there
is a continuous phase transition when the fourth order field is varied from
negative to positive values. This transition becomes discontinuous at low
temperatures. These two regimes are separated by a multicritical point. In the
case of competing four and eight fold fields, the first order transition at low
temperatures opens up into two Ising transitions. We then use numerical methods
to accurately locate the position of the multicritical point, and to verify the
nature of the transitions. The different techniques used include Monte Carlo
histogram methods combined with finite size scaling analysis, the real space
Monte Carlo Renormalization Group method, and the Monte Carlo Transfer Matrix
method. Our numerical results are in good agreement with the theoretical
arguments.Comment: 29 pages, HU-TFT-94-36, to appear in Phys. Rev. B, Vol 50, November
1, 1994. A LaTeX file with no figure
Equilibrium Shape and Size of Supported Heteroepitaxial Nanoislands
We study the equilibrium shape, shape transitions and optimal size of
strained heteroepitaxial nanoislands with a two-dimensional atomistic model
using simply adjustable interatomic pair potentials. We map out the global
phase diagram as a function of substrate-adsorbate misfit and interaction. This
phase diagram reveals all the phases corresponding to different well-known
growth modes. In particular, for large enough misfits and attractive substrate
there is a Stranski-Krastanow regime, where nano-sized islands grow on top of
wetting films. We analyze the various terms contributing to the total island
energy in detail, and show how the competition between them leads to the
optimal shape and size of the islands. Finally, we also develop an analytic
interpolation formula for the various contributions to the total energy of
strained nanoislands.Comment: 9 pages, 7 figure
Field-induced superconductor to insulator transition in Josephson-junction ladders
The superconductor to insulator transition is studied in a self-charging
model for a ladder of Josephson-junctions in presence of an external magnetic
field. Path integral Monte Carlo simulations of the equivalent
(1+1)-dimensional classical model are used to study the phase diagram and
critical behavior. In addition to a superconducting (vortex-free) phase, a
vortex phase can also occur for increasing magnetic field and small charging
energy. It is found that an intervening insulating phase separates the
superconducting from the vortex phases. Surprisingly, a finite-size scaling
analysis shows that the field-induced superconducting to insulator transition
is in the KT universality class even tough the external field breaks
time-reversal symmetry.Comment: 5 pages, 7 figures, to appear in Phys. Rev.
Current-voltage scaling of a Josephson-junction array at irrational frustration
Numerical simulations of the current-voltage characteristics of an ordered
two-dimensional Josephson junction array at an irrational flux quantum per
plaquette are presented. The results are consistent with an scaling analysis
which assumes a zero temperature vortex glass transition. The thermal
correlation length exponent characterizing this transition is found to be
significantly different from the corresponding value for vortex-glass models in
disordered two-dimensional superconductors. This leads to a current scale where
nonlinearities appear in the current-voltage characteristics decreasing with
temperature roughly as in contrast with the behavior expected
for disordered models.Comment: RevTex 3.0, 12 pages with Latex figures, to appear in Phys. Rev. B
54, Rapid. Com
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