440 research outputs found
Scaling, domains, and states in the four-dimensional random field Ising magnet
The four dimensional Gaussian random field Ising magnet is investigated
numerically at zero temperature, using samples up to size , to test
scaling theories and to investigate the nature of domain walls and the
thermodynamic limit. As the magnetization exponent is more easily
distinguishable from zero in four dimensions than in three dimensions, these
results provide a useful test of conventional scaling theories. Results are
presented for the critical behavior of the heat capacity, magnetization, and
stiffness. The fractal dimensions of the domain walls at criticality are
estimated. A notable difference from three dimensions is the structure of the
spin domains: frozen spins of both signs percolate at a disorder magnitude less
than the value at the ferromagnetic to paramagnetic transition. Hence, in the
vicinity of the transition, there are two percolating clusters of opposite
spins that are fixed under any boundary conditions. This structure changes the
interpretation of the domain walls for the four dimensional case. The scaling
of the effect of boundary conditions on the interior spin configuration is
found to be consistent with the domain wall dimension. There is no evidence of
a glassy phase: there appears to be a single transition from two ferromagnetic
states to a single paramagnetic state, as in three dimensions. The slowing down
of the ground state algorithm is also used to study this model and the links
between combinatorial optimization and critical behavior.Comment: 13 pages, 16 figure
Effects of Disorder on Electron Transport in Arrays of Quantum Dots
We investigate the zero-temperature transport of electrons in a model of
quantum dot arrays with a disordered background potential. One effect of the
disorder is that conduction through the array is possible only for voltages
across the array that exceed a critical voltage . We investigate the
behavior of arrays in three voltage regimes: below, at and above the critical
voltage. For voltages less than , we find that the features of the
invasion of charge onto the array depend on whether the dots have uniform or
varying capacitances. We compute the first conduction path at voltages just
above using a transfer-matrix style algorithm. It can be used to
elucidate the important energy and length scales. We find that the geometrical
structure of the first conducting path is essentially unaffected by the
addition of capacitive or tunneling resistance disorder. We also investigate
the effects of this added disorder to transport further above the threshold. We
use finite size scaling analysis to explore the nonlinear current-voltage
relationship near . The scaling of the current near ,
, gives similar values for the effective exponent
for all varieties of tunneling and capacitive disorder, when the current is
computed for voltages within a few percent of threshold. We do note that the
value of near the transition is not converged at this distance from
threshold and difficulties in obtaining its value in the limit
Exact Algorithm for Sampling the 2D Ising Spin Glass
A sampling algorithm is presented that generates spin glass configurations of
the 2D Edwards-Anderson Ising spin glass at finite temperature, with
probabilities proportional to their Boltzmann weights. Such an algorithm
overcomes the slow dynamics of direct simulation and can be used to study
long-range correlation functions and coarse-grained dynamics. The algorithm
uses a correspondence between spin configurations on a regular lattice and
dimer (edge) coverings of a related graph: Wilson's algorithm [D. B. Wilson,
Proc. 8th Symp. Discrete Algorithms 258, (1997)] for sampling dimer coverings
on a planar lattice is adapted to generate samplings for the dimer problem
corresponding to both planar and toroidal spin glass samples. This algorithm is
recursive: it computes probabilities for spins along a "separator" that divides
the sample in half. Given the spins on the separator, sample configurations for
the two separated halves are generated by further division and assignment. The
algorithm is simplified by using Pfaffian elimination, rather than Gaussian
elimination, for sampling dimer configurations. For n spins and given floating
point precision, the algorithm has an asymptotic run-time of O(n^{3/2}); it is
found that the required precision scales as inverse temperature and grows only
slowly with system size. Sample applications and benchmarking results are
presented for samples of size up to n=128^2, with fixed and periodic boundary
conditions.Comment: 18 pages, 10 figures, 1 table; minor clarification
Irrational mode locking in quasiperiodic systems
A model for ac-driven systems, based on the
Tang-Wiesenfeld-Bak-Coppersmith-Littlewood automaton for an elastic medium,
exhibits mode-locked steps with frequencies that are irrational multiples of
the drive frequency, when the pinning is spatially quasiperiodic. Detailed
numerical evidence is presented for the large-system-size convergence of such a
mode-locked step. The irrational mode locking is stable to small thermal noise
and weak disorder. Continuous time models with irrational mode locking and
possible experimental realizations are discussed.Comment: 4 pages, 3 figures, 1 table; revision: 2 figures modified, reference
added, minor clarification
Self-Organized Criticality in Non-Conserved Systems
The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic and neutrally stable. A change to open boundaries results in the invasion of the interior by a ``self-organized\u27\u27 region. The mechanism for the self-organization is closely related to the synchronization or phase-locking of the individual elements with each other. A simplified model of marginal oscillator locking on a directed lattice is used to explain many of the features in the non-conserved model: in particular, the dependence of the avalanche-distribution exponent on the conservation parameter is examined
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