410 research outputs found
Ground state of the random-bond spin-1 Heisenberg chain
Stochastic series expansion quantum Monte Carlo is used to study the ground
state of the antiferromagnetic spin-1 Heisenberg chain with bond disorder.
Typical spin- and string-correlations functions behave in accordance with
real-space renormalization group predictions for the random-singlet phase. The
average string-correlation function decays algebraically with an exponent of
-0.378(6), in very good agreement with the prediction of , while the average spin-correlation function is found to decay with an
exponent of about -1, quite different from the expected value of -2. By
implementing the concept of directed loops for the spin-1 chain we show that
autocorrelation times can be reduced by up to two orders of magnitude.Comment: 9 pages, 10 figure
Dynamics and transport in random quantum systems governed by strong-randomness fixed points
We present results on the low-frequency dynamical and transport properties of
random quantum systems whose low temperature (), low-energy behavior is
controlled by strong disorder fixed points. We obtain the momentum and
frequency dependent dynamic structure factor in the Random Singlet (RS) phases
of both spin-1/2 and spin-1 random antiferromagnetic chains, as well as in the
Random Dimer (RD) and Ising Antiferromagnetic (IAF) phases of spin-1/2 random
antiferromagnetic chains. We show that the RS phases are unusual `spin metals'
with divergent low-frequency spin conductivity at T=0, and we also follow the
conductivity through novel `metal-insulator' transitions tuned by the strength
of dimerization or Ising anisotropy in the spin-1/2 case, and by the strength
of disorder in the spin-1 case. We work out the average spin and energy
autocorrelations in the one-dimensional random transverse field Ising model in
the vicinity of its quantum critical point. All of the above calculations are
valid in the frequency dominated regime \omega \agt T, and rely on previously
available renormalization group schemes that describe these systems in terms of
the properties of certain strong-disorder fixed point theories. In addition, we
obtain some information about the behavior of the dynamic structure factor and
dynamical conductivity in the opposite `hydrodynamic' regime for
the special case of spin-1/2 chains close to the planar limit (the quantum x-y
model) by analyzing the corresponding quantities in an equivalent model of
spinless fermions with weak repulsive interactions and particle-hole symmetric
disorder.Comment: Long version (with many additional results) of Phys. Rev. Lett. {\bf
84}, 3434 (2000) (available as cond-mat/9904290); two-column format, 33 pages
and 8 figure
Current--Voltage Characteristics of Two--Dimensional Vortex Glass Models
We have performed Monte Carlo simulations to determine current--voltage
characteristics of two different vortex glass models in two dimensions. The
results confirm the conclusions of earlier studies that there is a transition
at . In addition we find that, as , the linear resistance vanishes
exponentially, and the current scale, , where non-linearities appear in
the -- characteristics varies roughly as , quite different from the
predictions of conventional flux creep theory, . The results for
the two models agree quite well with each other, and also agree fairly well
with recent experiments on very thin films of YBCO.Comment: 18 pages with 10 figures available upon request from R. A. Hyman at
[email protected]. The only change in the new version is the
deletion of an unimportant comment.IUCM94-01
Numerical renormalization-group study of spin correlations in one-dimensional random spin chains
We calculate the ground-state two-spin correlation functions of spin-1/2
quantum Heisenberg chains with random exchange couplings using the real-space
renormalization group scheme. We extend the conventional scheme to take account
of the contribution of local higher multiplet excitations in each decimation
step. This extended scheme can provide highly accurate numerical data for large
systems. The random average of staggered spin correlations of the chains with
random antiferromagnetic (AF) couplings shows algebraic decay like ,
which verifies the Fisher's analytic results. For chains with random
ferromagnetic (FM) and AF couplings, the random average of generalized
staggered correlations is found to decay more slowly than a power-law, in the
form close to . The difference between the distribution functions of
the spin correlations of the random AF chains and of the random FM-AF chains is
also discussed.Comment: 14 pages including 8 figures, REVTeX, submitted to Physical Review
Percolation in random environment
We consider bond percolation on the square lattice with perfectly correlated
random probabilities. According to scaling considerations, mapping to a random
walk problem and the results of Monte Carlo simulations the critical behavior
of the system with varying degree of disorder is governed by new, random fixed
points with anisotropic scaling properties. For weaker disorder both the
magnetization and the anisotropy exponents are non-universal, whereas for
strong enough disorder the system scales into an {\it infinite randomness fixed
point} in which the critical exponents are exactly known.Comment: 8 pages, 7 figure
Exact results for quantum phase transitions in random XY spin chains
The effect of disorder on the quantum phase transitions induced by a
transverse field, anisotropy, and dimerization in XY spin chains is
investigated. The low-energy behavior near the critical point is described by a
Dirac-type equation with a random mass for which an exact analytic treatment is
possible. Results obtained for the dynamical critical exponent, the specific
heat, and transverse susceptibility agree with results recently obtained using
a real space renormalization group decimation technique, supporting Fisher's
claim that it is exact. A non-zero transverse field changes the universality
class of the anisotropy transition.Comment: 5 pages, RevTeX + epsf, 2 figures
Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field
We present some exact results for the effect of disorder on the critical
properties of an anisotropic XY spin chain in a transverse field. The continuum
limit of the corresponding fermion model is taken and in various cases results
in a Dirac equation with a random mass. Exact analytic techniques can then be
used to evaluate the density of states and the localization length. In the
presence of disorder the ferromagnetic-paramagnetic or Ising transition of the
model is in the same universality class as the random transverse field Ising
model solved by Fisher using a real space renormalization group decimation
technique (RSRGDT). If there is only randomness in the anisotropy of the
magnetic exchange then the anisotropy transition (from a ferromagnet in the
direction to a ferromagnet in the direction) is also in this universality
class. However, if there is randomness in the isotropic part of the exchange or
in the transverse field then in a non-zero transverse field the anisotropy
transition is destroyed by the disorder. We show that in the Griffiths' phase
near the Ising transition that the ground state energy has an essential
singularity. The results obtained for the dynamical critical exponent, the
typical correlation length, and the temperature dependence of the specific heat
near the Ising transition agree with the results of the RSRGDT and numerical
work.Comment: 22 pages, RevTeX + epsf, 4 figure
Monte Carlo calculation of the current-voltage characteristics of a two dimensional lattice Coulomb gas
We have studied the nonlinear current-voltage characteristic of a two
dimensional lattice Coulomb gas by Monte Carlo simulation. We present three
different determinations of the power-law exponent of the nonlinear
current-voltage characteristic, . The determinations rely on
both equilibrium and non-equilibrium simulations. We find good agreement
between the different determinations, and our results also agree closely with
experimental results for Hg-Xe thin film superconductors and for certain single
crystal thin-film high temperature superconductors.Comment: late
XY models with disorder and symmetry-breaking fields in two dimensions
The combined effect of disorder and symmetry-breaking fields on the
two-dimensional XY model is examined. The study includes disorder in the
interaction among spins in the form of random phase shifts as well as disorder
in the local orientation of the field. The phase diagrams are determined and
the properties of the various phases and phase transitions are calculated. We
use a renormalization group approach in the Coulomb gas representation of the
model. Our results differ from those obtained for special cases in previous
works. In particular, we find a changed topology of the phase diagram that is
composed of phases with long-range order, quasi-long-range order, and
short-range order. The discrepancies can be ascribed to a breakdown of the
fugacity expansion in the Coulomb gas representation.
Implications for physical systems such as planar Josephson junctions and the
faceting of crystal surfaces are discussed.Comment: 17 pages Latex with 5 eps figures, change: acknowledgment extende
Finite-temperature resistive transition in the two-dimensional XY gauge glass model
We investigate numerically the resistive transition in the two-dimensional XY
gauge glass model. The resistively-shunted junction dynamics subject to the
fluctuating twist boundary condition is used and the linear resistances in the
absence of an external current at various system sizes are computed. Through
the use of the standard finite-size scaling method, the finite temperature
resistive transition is found at (in units of the Josephson
coupling strength) with dynamic critical exponent and the static
exponent , in contrast to widely believed expectation of the
zero-temperature transition. Comparisons with existing experiments and
simulations are also made.Comment: 5 pages in two columns, 4 eps figures included, to appear in PR
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