739 research outputs found
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
Two spin liquid phases in the spatially anisotropic triangular Heisenberg model
The quantum spin-1/2 antiferromagnetic Heisenberg model on a two dimensional
triangular lattice geometry with spatial anisotropy is relevant to describe
materials like and organic compounds like
{-(ET)Cu(CN)}. The strength of the spatial anisotropy can
increase quantum fluctuations and can destabilize the magnetically ordered
state leading to non conventional spin liquid phases. In order to understand
these intriguing phenomena, quantum Monte Carlo methods are used to study this
model system as a function of the anisotropic strength, represented by the
ratio between the intra-chain nearest neighbor coupling and the
inter-chain one . We have found evidence of two spin liquid regions. The
first one is stable for small values of the coupling J'/J \alt 0.65, and
appears gapless and fractionalized, whereas the second one is a more
conventional spin liquid with a small spin gap and is energetically favored in
the region 0.65\alt J'/J \alt 0.8. We have also shown that in both spin
liquid phases there is no evidence of broken translation symmetry with dimer or
spin-Peirls order or any broken spatial reflection symmetry of the lattice. The
various phases are in good agreement with the experimental findings, thus
supporting the existence of spin liquid phases in two dimensional quantum
spin-1/2 systems.Comment: 35 pages, 24 figures, 3 table
One-loop approximation for the Heisenberg antiferromagnet
We use the diagram technique for spin operators to calculate Green's
functions and observables of the spin-1/2 quantum Heisenberg antiferromagnet on
a square lattice. The first corrections to the self-energy and interaction are
taken into account in the chain diagrams. The approximation reproduces main
results of Takahashi's modified spin-wave theory [Phys. Rev. B 40, 2494 (1989)]
and is applicable in a wider temperature range. The energy per spin calculated
in this approximation is in good agreement with the Monte Carlo and
small-cluster exact-diagonalization calculations in the range 0 <= T < 1.2J
where J is the exchange constant. For the static uniform susceptibility the
agreement is good for T < 0.6J and becomes somewhat worse for higher
temperatures. Nevertheless the approximation is able to reproduce the maximum
in the temperature dependence of the susceptibility near T = 0.9J.Comment: 15 pages, 6 ps figure
The influence of critical behavior on the spin glass phase
We have argued in recent papers that Monte Carlo results for the equilibrium
properties of the Edwards-Anderson spin glass in three dimensions, which had
been interpreted earlier as providing evidence for replica symmetry breaking,
can be explained quite simply within the droplet model once finite size effects
and proximity to the critical point are taken into account. In this paper, we
show that similar considerations are sufficient to explain the Monte Carlo data
in four dimensions. In particular, we study the Parisi overlap and the link
overlap for the four-dimensional Ising spin glass in the Migdal-Kadanoff
approximation. Similar to what is seen in three dimensions, we find that
temperatures well below those studied in Monte Carlo simulations have to be
reached before the droplet model predictions become apparent. We also show that
the double-peak structure of the link overlap distribution function is related
to the difference between domain-wall excitations that cross the entire system
and droplet excitations that are confined to a smaller region.Comment: 8 pages, 8 figure
Critical temperature and the transition from quantum to classical order parameter fluctuations in the three-dimensional Heisenberg antiferromagnet
We present results of extensive quantum Monte Carlo simulations of the
three-dimensional (3D) S=1/2 Heisenberg antiferromagnet. Finite-size scaling of
the spin stiffness and the sublattice magnetization gives the critical
temperature Tc/J = 0.946 +/- 0.001. The critical behavior is consistent with
the classical 3D Heisenberg universality class, as expected. We discuss the
general nature of the transition from quantum mechanical to classical (thermal)
order parameter fluctuations at a continuous Tc > 0 phase transition.Comment: 5 pages, Revtex, 4 PostScript figures include
Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet
We have studied the antiferromagnetic order -- disorder transition occurring
at in a 2-layer quantum Heisenberg antiferromagnet as the inter-plane
coupling is increased. Quantum Monte Carlo results for the staggered structure
factor in combination with finite-size scaling theory give the critical ratio
between the inter-plane and in-plane coupling constants.
The critical behavior is consistent with the 3D classical Heisenberg
universality class. Results for the uniform magnetic susceptibility and the
correlation length at finite temperature are compared with recent predictions
for the 2+1-dimensional nonlinear -model. The susceptibility is found
to exhibit quantum critical behavior at temperatures significantly higher than
the correlation length.Comment: 11 pages (5 postscript figures available upon request), Revtex 3.
Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
The ground state parameters of the two-dimensional S=1/2 antiferromagnetic
Heisenberg model are calculated using the Stochastic Series Expansion quantum
Monte Carlo method for L*L lattices with L up to 16. The finite-size results
for the energy E, the sublattice magnetization M, the long-wavelength
susceptibility chi_perp(q=2*pi/L), and the spin stiffness rho_s, are
extrapolated to the thermodynamic limit using fits to polynomials in 1/L,
constrained by scaling forms previously obtained from renormalization group
calculations for the nonlinear sigma model and chiral perturbation theory. The
results are fully consistent with the predicted leading finite-size corrections
and are of sufficient accuracy for extracting also subleading terms. The
subleading energy correction (proportional to 1/L^4) agrees with chiral
perturbation theory to within a statistical error of a few percent, thus
providing the first numerical confirmation of the finite-size scaling forms to
this order. The extrapolated ground state energy per spin, E=-0.669437(5), is
the most accurate estimate reported to date. The most accurate Green's function
Monte Carlo (GFMC) result is slightly higher than this value, most likely due
to a small systematic error originating from ``population control'' bias in
GFMC. The other extrapolated parameters are M=0.3070(3), rho_s = 0.175(2),
chi_perp = 0.0625(9), and the spinwave velocity c=1.673(7). The statistical
errors are comparable with those of the best previous estimates, obtained by
fitting loop algorithm quantum Monte Carlo data to finite-temperature scaling
forms. Both M and rho_s obtained from the finite-T data are, however, a few
error bars higher than the present estimates. It is argued that the T=0
extrapolations performed here are less sensitive to effects of neglectedComment: 16 pages, RevTex, 9 PostScript figure
Trivial Ground State Structure in the Two-Dimensional Ising Spin Glass
We study how the ground state of the two-dimensional Ising spin glass with
Gaussian interactions in zero magnetic field changes on altering the boundary
conditions. The probability that relative spin orientations change in a region
far from the boundary goes to zero with the (linear) size of the system L like
L^{-lambda}, where lambda = -0.70 +/- 0.08. We argue that lambda is equal to
d-d_f where d (=2) is the dimension of the system and d_f is the fractal
dimension of a domain wall induced by changes in the boundary conditions. Our
value for d_f is consistent with earlier estimates. These results show that, at
zero temperature, there is only a single pure state (plus the state with all
spins flipped) in agreement with the predictions of the droplet model.Comment: 4 pages, 3 postscript figures; some changes in response to referees'
comments, to appear in Phys Rev. B, Rapid Communications, Oct.
Ising Expansion for the Hubbard Model
We develop series expansions for the ground state properties of the Hubbard
model, by introducing an Ising anisotropy into the Hamiltonian. For the
two-dimensional (2D) square lattice half-filled Hubbard model, the ground state
energy, local moment, sublattice magnetization, uniform magnetic susceptibility
and spin stiffness are calculated as a function of , where is the
Coulomb constant and is the hopping parameter. Magnetic susceptibility data
indicate a crossover around between spin density wave
antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte
Carlo simulations, RPA result and mean field solutions are also made.Comment: 22 pages, 6 Postscript figures, Revte
Spin Dynamics of La_2CuO_4 and the Two-Dimensional Heisenberg Model
The spin-lattice relaxation rate and the spin echo decay rate
for the 2D Heisenberg model are calculated using quantum Monte Carlo
and maximum entropy analytic continuation. The results are compared to recent
experiments on LaCuO, as well as predictions based on the non-linear
-model.Comment: Compressed & uuencoded Postscript file (4 pages with figures
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