1,367 research outputs found
Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D Random-Bond Ising Model
The statistics of the ground-state and domain-wall energies for the
two-dimensional random-bond Ising model on square lattices with independent,
identically distributed bonds of probability of and of
are studied. We are able to consider large samples of up to
spins by using sophisticated matching algorithms. We study
systems, but we also consider samples, for different aspect ratios
. We find that the scaling behavior of the ground-state energy and
its sample-to-sample fluctuations inside the spin-glass region () are characterized by simple scaling functions. In particular, the
fluctuations exhibit a cusp-like singularity at . Inside the spin-glass
region the average domain-wall energy converges to a finite nonzero value as
the sample size becomes infinite, holding fixed. Here, large finite-size
effects are visible, which can be explained for all by a single exponent
, provided higher-order corrections to scaling are included.
Finally, we confirm the validity of aspect-ratio scaling for : the
distribution of the domain-wall energies converges to a Gaussian for ,
although the domain walls of neighboring subsystems of size are
not independent.Comment: 11 pages with 15 figures, extensively revise
Background gauge invariance in the antifield formalism for theories with open gauge algebras
We show that any BRST invariant quantum action with open or closed gauge
algebra has a corresponding local background gauge invariance. If the BRST
symmetry is anomalous, but the anomaly can be removed in the antifield
formalism, then the effective action possesses a local background gauge
invariance. The presence of antifields (BRST sources) is necessary. As an
example we analyze chiral gravity.Comment: 17pp., Latex, mispelling in my name! corrected, no other change
Power-law correlations and orientational glass in random-field Heisenberg models
Monte Carlo simulations have been used to study a discretized Heisenberg
ferromagnet (FM) in a random field on simple cubic lattices. The spin variable
on each site is chosen from the twelve [110] directions. The random field has
infinite strength and a random direction on a fraction x of the sites of the
lattice, and is zero on the remaining sites. For x = 0 there are two phase
transitions. At low temperatures there is a [110] FM phase, and at intermediate
temperature there is a [111] FM phase. For x > 0 there is an intermediate phase
between the paramagnet and the ferromagnet, which is characterized by a
|k|^(-3) decay of two-spin correlations, but no true FM order. The [111] FM
phase becomes unstable at a small value of x. At x = 1/8 the [110] FM phase has
disappeared, but the power-law correlated phase survives.Comment: 8 pages, 12 Postscript figure
Random Field Models for Relaxor Ferroelectric Behavior
Heat bath Monte Carlo simulations have been used to study a four-state clock
model with a type of random field on simple cubic lattices. The model has the
standard nonrandom two-spin exchange term with coupling energy and a random
field which consists of adding an energy to one of the four spin states,
chosen randomly at each site. This Ashkin-Teller-like model does not separate;
the two random-field Ising model components are coupled. When , the
ground states of the model remain fully aligned. When , a
different type of ground state is found, in which the occupation of two of the
four spin states is close to 50%, and the other two are nearly absent. This
means that one of the Ising components is almost completely ordered, while the
other one has only short-range correlations. A large peak in the structure
factor appears at small for temperatures well above the transition
to long-range order, and the appearance of this peak is associated with slow,
"glassy" dynamics. The phase transition into the state where one Ising
component is long-range ordered appears to be first order, but the latent heat
is very small.Comment: 7 pages + 12 eps figures, to appear in Phys Rev
Power-law correlated phase in random-field XY models and randomly pinned charge-density waves
Monte Carlo simulations have been used to study the Z6 ferromagnet in a
random field on simple cubic lattices, which is a simple model for randomly
pinned charge-density waves. The random field is chosen to have infinite
strength on a fraction x of the sites of the lattice, and to be zero on the
remaining sites. For x= 1/16 there are two phase transitions. At low
temperature there is a ferromagnetic phase, which is stabilized by the six-fold
nonrandom anisotropy. The intermediate temperature phase is characterized by a
|k|^(-3) decay of two-spin correlations, but no true ferromagnetic order. At
the transition between the power-law correlated phase and the paramagnetic
phase the magnetic susceptibility diverges, and the two-spin correlations decay
approximately as |k|^(-2.87).Comment: 16 pages, 8 figures, Postscrip
Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors
As a simplified model of randomly pinned vortex lattices or charge-density
waves, we study the random-field XY model on square () and simple cubic
() lattices. We verify in Monte Carlo simulations, that the average
spacing between topological defects (vortices) diverges more strongly than the
Imry-Ma pinning length as the random field strength, , is reduced. We
suggest that for the simulation data are consistent with a topological
phase transition at a nonzero critical field, , to a pinned phase that is
defect-free at large length-scales. We also discuss the connection between the
possible existence of this phase transition in the random-field XY model and
the magnetic field driven transition from pinned vortex lattice to vortex glass
in weakly disordered type-II superconductors.Comment: LATEX file; 5 Postscript figures are available from [email protected]
Finite-Size Scaling in the Energy-Entropy Plane for the 2D +- J Ising Spin Glass
For square lattices with the 2D Ising spin glass with
+1 and -1 bonds is found to have a strong correlation between the energy and
the entropy of its ground states. A fit to the data gives the result that each
additional broken bond in the ground state of a particular sample of random
bonds increases the ground state degeneracy by approximately a factor of 10/3.
For (where is the fraction of negative bonds), over this range of
, the characteristic entropy defined by the energy-entropy correlation
scales with size as . Anomalous scaling is not found for the
characteristic energy, which essentially scales as . When , a
crossover to scaling of the entropy is seen near . The results
found here suggest a natural mechanism for the unusual behavior of the low
temperature specific heat of this model, and illustrate the dangers of
extrapolating from small .Comment: 9 pages, two-column format; to appear in J. Statistical Physic
Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond 8-state Potts Model
The self-dual random-bond eight-state Potts model is studied numerically
through large-scale Monte Carlo simulations using the Swendsen-Wang cluster
flipping algorithm. We compute bulk and surface order parameters and
susceptibilities and deduce the corresponding critical exponents at the random
fixed point using standard finite-size scaling techniques. The scaling laws are
suitably satisfied. We find that a belonging of the model to the 2D Ising model
universality class can be conclusively ruled out, and the dimensions of the
relevant bulk and surface scaling fields are found to take the values
, , , to be compared to their Ising values:
15/8, 1, and 1/2.Comment: LaTeX file with Revtex, 4 pages, 4 eps figures, to appear in Phys.
Rev. Let
Deterministic Soluble Model of Coarsening
We investigate a 3-phase deterministic one-dimensional phase ordering model
in which interfaces move ballistically and annihilate upon colliding. We
determine analytically the autocorrelation function A(t). This is done by
computing generalized first-passage type probabilities P_n(t) which measure the
fraction of space crossed by exactly n interfaces during the time interval
(0,t), and then expressing the autocorrelation function via P_n's. We further
reveal the spatial structure of the system by analyzing the domain size
distribution.Comment: 5 pages, RevTeX fil
Ionic liquid crystals : synthesis and characterization via NMR, DSC, POM, X-ray diffraction and ionic conductivity of asymmetric viologen bistriflimide salts
Acknowledgments This research is in part supported by the NSF EPSCoR RING-TRUE III grant no. 0447416, NSF-SBIR grant no. OII-0610753, NSF-STTR grant no. IIP-0740289 and NASA GRC contract no. NNX10CD25P (PKB). We thank Ronald C. G. Principe for making the Figures and Tables for this article. Acknowledgment is made to the donors of the American Chemical Society Petroleum Research Fund grant no. 59345-ND7 for partial support of this research by CMR and MRF. AMF would like to thank the Carnegie Trust for the Universities of Scotland, for the Research Incentive Grant RIG008586, the Royal Society and Specac Ltd., for the Research Grant RGS\R1\201397, and the Royal Society of Chemistry for the award of a mobility grant (M19-0000).Peer reviewedPostprin
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