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Spin Glasses
Work in collaboration with Alain Billoire (Saclay) and Wolfhard Janke (Leipzig).
Spin glasses
constitute an important class of materials whose
low-temperature state is a frozen disordered one. In order to produce
such a state, there must be randomness and frustration among the
different interactions between the spins (magnetic moments).
Frustration means that no single spin configuration is favored by
all interactions. In real materials such competing interactions are
for instance created by magnetic impurity moments.
The study of spin glasses developed essentially since the middle of
the 1970's and is based on three approaches: experiment, theory and
computer simulation.
Experimentally it is not hard to find spin glasses. One
kind of widely studied systems consists of dilute solutions of
transition
metal magnetic impurities in noble hosts. The impurity moments
produce a magnetic polarization of the host metal conduction electrons
which is positive at some distances and negative at others.
Because of the random placements of the impurities they have random,
competing interactions with one another. Spin glass states have also
been found in magnetic insulators and amorphous alloys. Properties
analogous to those of spin glasses, with the electric dipole moment
playing the role of the magnetic one, have been seen in
ferroelectric-antiferroelectric mixtures. The universal behavior of
the observed phenomena is a major reason for the interest in these
systems.
A freezing temperature $T_c$ may be
defined by a cusp in the ac susceptibility and has, for instance, been
studied for Cu-0.9. Below this transition temperature
characteristic non-equilibrium phenomena are observed. A typical
experiment is the measurement of the remanent magnetization.
A spin-glass sample is rapidly cooled in a magnetic field
to a temperature below the transition temperature and the observation
is that the decay of the magnetization depends on the waiting time
after which the field is switched off. This phenomenon
is called aging and has also been found in
other disordered or amorphous systems such as structural glasses,
polymers, high-temperature superconductors, and charge-density wave
systems. These large characteristic time scales suggest the presence
of many equilibrium or metastable configurations with a distribution
of free-energy barriers separating them.
Our work contributes to the numerical studies of these barriers. It employes the multi-overlap algorithm ( cond-mat/9712320 or PRL ) of Berg and Janke, which belongs to the class of multicanonical algorithms. Berg, Billoire and Janke performed large scale simulation on the T3E computer of CEA in Grenoble, France and on T3E computers in Germany. Preliminary results were reported in Annalen der Physik ( cond-mat/9811423). Recently, an analysis of the free energy barriers of Edward-Anderson Ising spin glass in three and four dimensions was completed ( cond-mat/9910323) or PRB 61 (2000) 12143). The following animation Spin Glass RealizationsRecently we have investigated the fall-off behavior properties of the Parisi overlap density in som details and found some amazing relationships with the statistics of extremes ( cond-mat/0108034 or PRE 65 (2002) 045102R).
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