Defect energies and spin stiffness for continuous spin glasses
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Considerable advances have been made in recent years in the understanding of Ising
spin glass models in two and three dimensions. Models with continuous
degrees-of-freedom, which are often more realistic in describing physical systems,
have received much less attention. To make progress in this direction, the
two-dimensional XY spin-glass model with bimodal coupling distribution is
investigated by applying a novel ``embedded matching'' technique augmented by a
specially tailored genetic algorithm to find numerically exact ground-state
configurations for relatively large systems of up to $2828$ spins. Perhaps
surprisingly, the resulting ground states are found to be non-generate, implying a
critical exponent $= 0$. The spin-glass phase at zero temperature is described
by the scaling of the spin stiffness as determined from the energy differences
between ground states of systems with different boundary conditions. Owned to the
novel technique and the consequently larger accessible system sizes as well as
elaborate finite-size scaling techniques, the corresponding spin-stiffness exponent
$þeta_s$ is for the first time determined consistently from different sets of
boundary conditions. Considering the stiffness of the system towards chiral
excitations, a result different from the spin stiffness is found, strongly indicating
the presence of spin-chirality decoupling~1,2. The nature of the spin-glass phase
is investigated in terms of the fractal dimension of chiral and spin domain walls, as
well as the plain and windowed overlaps of ground-state configurations~3.
Generalizations of the proposed genetic embedded matching technique to the case of
spin glasses on non-planar lattices are considered. Replacing the matching component
with an appropriate variant of a local spin-quench approach combined with an element
of over-relaxation allows to find exact ground states for a three-dimensional
Heisenberg spin glass for systems up to $161616$ spins~4. The
resulting estimates of spin and chiral stiffness exponents are contrasted with
results for spin and chiral ordering in the Heisenberg spin glass as found from
finite-temperature Monte Carlo simulations.
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ıtem91193 M. Weigel and M. J. P. Gingras, Phys. Rev. Lett. 96, 097206 (2006).
ıtem91293 M. Weigel and M. J. P. Gingras, J. Phys.: Condens. Matter 19,
145217 (2007).
ıtem91393 M. Weigel and M. J. P. Gingras, in preparation.
ıtem91493 M. Weigel, in preparation.
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