4,827 research outputs found
Zero-Temperature Configurations of Short Odd-Numbered Classical Spin Chains with Bilinear and Biquadratic Exchange Interactions
The lowest energy configurations of short odd open chains with classical
spins are determined for antiferromagnetic bilinear and biquadratic
nearest-neighbor exchange interactions. The zero field residual magnetization
generates differences with the magnetic behavior of even chains, as the odd
chain is like a small magnet for weak magnetic fields. The lowest energy
configuration is calculated as a function of the total magnetization M, even
for M less than the zero field residual magnetization. Analytic expressions and
their proofs are provided for the threshold magnetic field needed to drive the
system away from the antiferromagnetic configuration and the spin polar angles
in its vicinity, when the biquadratic interaction is relatively weak. They are
also given for the saturation magnetic field and the spin polar angles close to
it. Finally, an analytic expression along with its proof is given for the
maximum magnetization in zero magnetic field for stronger biquadratic
interaction, where the lowest energy configuration is highly degenerate.Comment: 17 pages, 9 figure
Thermalization away from Integrability and the Role of Operator Off-Diagonal Elements
We investigate the rate of thermalization of local operators in the
one-dimensional anisotropic antiferromagnetic Heisenberg model with
next-nearest neighbor interactions that break integrability. This is done by
calculating the scaling of the difference of the diagonal and canonical thermal
ensemble values as function of system size, and by directly calculating the
time evolution of the expectation values of the operators with the Chebyshev
polynomial expansion. Spatial and spin symmetry is exploited and the
Hamiltonian is divided in subsectors according to their symmetry. The rate of
thermalization depends on the proximity to the integrable limit. When
integrability is weakly broken thermalization is slow, and becomes faster the
stronger the next-nearest neighbor interaction is. Three different regimes for
the rate of thermalization with respect to the strength of the integrability
breaking parameter are identified. These are shown to be directly connected
with the relative strength of the low and higher energy difference off-diagonal
operator matrix elements in the symmetry eigenbasis of the Hamiltonian. Close
to the integrable limit the off-diagonal matrix elements peak at higher
energies and high frequency fluctuations are important and slow down
thermalization. Away from the integrable limit a strong low energy peak
gradually develops that takes over the higher frequency fluctuations and leads
to quicker thermalization.Comment: 11 pages, 9 figure
Origin of the classical magnetization discontinuities of the dodecahedron
The classical antiferromagnetic Heisenberg model on the dodecahedron has been
shown to have three magnetization discontinuities in an external field. Here it
is shown that the highest-field discontinuity can be directly traced back to
the strong magnetization jump leading to saturation at the Ising limit, which
originates from the frustrated connectivity of the molecule. This discontinuity
survives up to the limit and disappears just before the ferromagnetic
Ising interaction fully polarizes the spins. The two lower-field jumps of the
model result from the competition of discontinuities that emerge from the
magnetization plateau surviving away from the Ising limit.Comment: 6 pages, 10 figure
- …