5,161 research outputs found
Damage spreading in two dimensional geometrically frustrated lattices: the triangular and kagome anistropic Heisenberg model
The technique of damage spreading is used to study the phase diagram of the
easy axis anisotropic Heisenberg antiferromagnet on two geometrically
frustrated lattices. The triangular and kagome systems are built up from
triangular units that either share edges or corners respectively. The
triangular lattice undergoes two sequential Kosterlitz-Thouless transitions
while the kagome lattice undergoes a glassy transition. In both cases, the
phase boundaries obtained using damage spreading are in good agreement with
those obtained from equilibrium Monte Carlo simulations.Comment: 7 pages, 4 figure
Spin Stiffness of Stacked Triangular Antiferromagnets
We study the spin stiffness of stacked triangular antiferromagnets using both
heat bath and broad histogram Monte Carlo methods. Our results are consistent
with a continuous transition belonging to the chiral universality class first
proposed by Kawamura.Comment: 5 pages, 7 figure
Z_2-vortex ordering of the triangular-lattice Heisenberg antiferromagnet
Ordering of the classical Heisenberg antiferromagnet on the triangular
lattice is studied by means of a mean-field calculation, a scaling argument and
a Monte Carlo simulation, with special attention to its vortex degree of
freedom. The model exhibits a thermodynamic transition driven by the Z_2-vortex
binding-unbinding, at which various thermodynamic quantities exhibit an
essential singularity. The low-temperature state is a "spin-gel" state with a
long but finite spin correlation length where the ergodicity is broken
topologically. Implications to recent experiments on triangular-lattice
Heisenberg antiferromagnets are discussed
Low-Temperature Excitations of Dilute Lattice Spin Glasses
A new approach to exploring low-temperature excitations in finite-dimensional
lattice spin glasses is proposed. By focusing on bond-diluted lattices just
above the percolation threshold, large system sizes can be obtained which
lead to enhanced scaling regimes and more accurate exponents. Furthermore, this
method in principle remains practical for any dimension, yielding exponents
that so far have been elusive. This approach is demonstrated by determining the
stiffness exponent for dimensions , (the upper critical dimension),
and . Key is the application of an exact reduction algorithm, which
eliminates a large fraction of spins, so that the reduced lattices never exceed
variables for sizes as large as L=30 in , L=9 in , or L=8
in . Finite size scaling analysis gives for ,
significantly improving on previous work. The results for and ,
and , are entirely new and are compared with
mean-field predictions made for d>=6.Comment: 7 pages, LaTex, 7 ps-figures included, added result for stiffness in
d=7, as to appear in Europhysics Letters (see
http://www.physics.emory.edu/faculty/boettcher/ for related information
Vortex-induced topological transition of the bilinear-biquadratic Heisenberg antiferromagnet on the triangular lattice
The ordering of the classical Heisenberg antiferromagnet on the triangular
lattice with the the bilinear-biquadratic interaction is studied by Monte Carlo
simulations. It is shown that the model exhibits a topological phase transition
at a finite-temperature driven by topologically stable vortices, while the spin
correlation length remains finite even at and below the transition point. The
relevant vortices could be of three different types, depending on the value of
the biquadratic coupling. Implications to recent experiments on the triangular
antiferromagnet NiGaS is discussed
Monte Carlo Study of the Anisotropic Heisenberg Antiferromagnet on the Triangular Lattice
We report a Monte Carlo study of the classical antiferromagnetic Heisenberg
model with easy axis anisotropy on the triangular lattice. Both the free energy
cost for long wavelength spin waves as well as for the formation of free
vortices are obtained from the spin stiffness and vorticity modulus
respectively. Evidence for two distinct Kosterlitz-Thouless types of
defect-mediated phase transitions at finite temperatures is presented.Comment: 8 pages, 10 figure
First-Order Transition to Incommensurate Phase with Broken Lattice Rotation Symmetry in Frustrated Heisenberg Model
We study a finite-temperature phase transition in the two-dimensional
classical Heisenberg model on a triangular lattice with a ferromagnetic
nearest-neighbor interaction and an antiferromagnetic
third-nearest-neighbor interaction using a Monte Carlo method. Apart from
a trivial degeneracy corresponding to O(3) spin rotations,the ground state for
has a threefold degeneracy corresponding to 120 degree lattice
rotations. We find that this model exhibits a first-order phase transition with
the breaking of the threefold symmetry when the interaction ratio is
.Comment: 4pages,5figure
Evidence for the droplet/scaling picture of spin glasses
We have studied the Parisi overlap distribution for the three dimensional
Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T
around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the
full Parisi replica symmetry breaking, just as was also observed in recent
Monte Carlo simulations on a cubic lattice. However, for lower temperatures our
data agree with predictions from the droplet or scaling picture. The failure to
see droplet model behaviour in Monte Carlo simulations is due to the fact that
all existing simulations have been done at temperatures too close to the
transition temperature so that sytem sizes larger than the correlation length
have not been achieved.Comment: 4 pages, 6 figure
- …