79,917 research outputs found
Generating droplets in two-dimensional Ising spin glasses by using matching algorithms
We study the behavior of droplets for two dimensional Ising spin glasses with
Gaussian interactions. We use an exact matching algorithm which enables study
of systems with linear dimension L up to 240, which is larger than is possible
with other approaches. But the method only allows certain classes of droplets
to be generated. We study single-bond, cross and a category of fixed volume
droplets as well as first excitations. By comparison with similar or equivalent
droplets generated in previous works, the advantages but also the limitations
of this approach are revealed. In particular we have studied the scaling
behavior of the droplet energies and droplet sizes. In most cases, a crossover
of the data can be observed such that for large sizes the behavior is
compatible with the one-exponent scenario of the droplet theory. Only for the
case of first excitations, no clear conclusion can be reached, probably because
even with the matching approach the accessible system sizes are still too
small.Comment: 11 pages, 16 figures, revte
RVB gauge theory and the Topological degeneracy in the Honeycomb Kitaev model
We relate the Z gauge theory formalism of the Kitaev model to the SU(2)
gauge theory of the resonating valence bond (RVB) physics. Further, we
reformulate a known Jordan-Wigner transformation of Kitaev model on a torus in
a general way that shows that it can be thought of as a Z gauge fixing
procedure. The conserved quantities simplify in terms of the gauge invariant
Jordan-Wigner fermions, enabling us to construct exact eigen states and
calculate physical quantities. We calculate the fermionic spectrum for flux
free sector for different gauge field configurations and show that the ground
state is four-fold degenerate on a torus in thermodynamic limit. Further on a
torus we construct four mutually anti-commuting operators which enable us to
prove that all eigenstates of this model are four fold degenerate in
thermodynamic limit.Comment: 12 pages, 3 figures. Added affiliation and a new section,
'Acknowledgements'.Typos correcte
Obtaining Stiffness Exponents from Bond-diluted Lattice Spin Glasses
Recently, a method has been proposed to obtain accurate predictions for
low-temperature properties of lattice spin glasses that is practical even above
the upper critical dimension, . This method is based on the observation
that bond-dilution enables the numerical treatment of larger lattices, and that
the subsequent combination of such data at various bond densities into a
finite-size scaling Ansatz produces more robust scaling behavior. In the
present study we test the potential of such a procedure, in particular, to
obtain the stiffness exponent for the hierarchical Migdal-Kadanoff lattice.
Critical exponents for this model are known with great accuracy and any
simulations can be executed to very large lattice sizes at almost any bond
density, effecting a insightful comparison that highlights the advantages -- as
well as the weaknesses -- of this method. These insights are applied to the
Edwards-Anderson model in with Gaussian bonds.Comment: corrected version, 10 pages, RevTex4, 12 ps-figures included; related
papers available a http://www.physics.emory.edu/faculty/boettcher
Invaded cluster algorithm for Potts models
The invaded cluster algorithm, a new method for simulating phase transitions,
is described in detail. Theoretical, albeit nonrigorous, justification of the
method is presented and the algorithm is applied to Potts models in two and
three dimensions. The algorithm is shown to be useful for both first-order and
continuous transitions and evidently provides an efficient way to distinguish
between these possibilities. The dynamic properties of the invaded cluster
algorithm are studied. Numerical evidence suggests that the algorithm has no
critical slowing for Ising models.Comment: 39 pages, revtex, 15 figures available on request from
[email protected], to appear in Phys. Rev.
- …