151 research outputs found
Pyridazines. LXII. Tetrazolo-Azido Equilibria of Tetrazolo[1,5-b ]pyridazines
Tetrazolo[l,5-b]pyridazines exist in solution exclusively in the
tetrazolo form. In solutions of strong acids an equilibrium of both
forms, azido and tetrazolo, is established. The equilibrium constants
in concentrated sulfuric acid or in trifluoromethanesulfonic acid
were determined
Dynamics of relaxor ferroelectrics
We study a dynamic model of relaxor ferroelectrics based on the spherical
random-bond---random-field model and the Langevin equations of motion. The
solution to these equations is obtained in the long-time limit where the system
reaches an equilibrium state in the presence of random local electric fields.
The complex dynamic linear and third-order nonlinear susceptibilities
and , respectively, are calculated as
functions of frequency and temperature. In analogy with the static case, the
dynamic model predicts a narrow frequency dependent peak in ,
which mimics a transition into a glass-like state.Comment: 15 pages, Revtex plus 5 eps figure
Random Field Models for Relaxor Ferroelectric Behavior
Heat bath Monte Carlo simulations have been used to study a four-state clock
model with a type of random field on simple cubic lattices. The model has the
standard nonrandom two-spin exchange term with coupling energy and a random
field which consists of adding an energy to one of the four spin states,
chosen randomly at each site. This Ashkin-Teller-like model does not separate;
the two random-field Ising model components are coupled. When , the
ground states of the model remain fully aligned. When , a
different type of ground state is found, in which the occupation of two of the
four spin states is close to 50%, and the other two are nearly absent. This
means that one of the Ising components is almost completely ordered, while the
other one has only short-range correlations. A large peak in the structure
factor appears at small for temperatures well above the transition
to long-range order, and the appearance of this peak is associated with slow,
"glassy" dynamics. The phase transition into the state where one Ising
component is long-range ordered appears to be first order, but the latent heat
is very small.Comment: 7 pages + 12 eps figures, to appear in Phys Rev
Classical transverse Ising spin glass with short- range interaction beyond the mean field approximation
The classical transverse field Ising spin- glass model with short-range
interactions is investigated beyond the mean- field approximation for a real d-
dimensional lattice. We use an appropriate nontrivial modification of the
Bethe- Peierls method recently formulated for the Ising spin- glass. The zero-
temperature critical value of the transverse field and the linear
susceptibility in the paramagnetic phase are obtained analytically as functions
of dimensionality d. The phase diagram is also calculated numerically for
different values of d. In the limit d -> infinity, known mean- field results
are consistently reproduced.Comment: LaTex, 11 pages, 2 figure
Tricritical Points in the Sherrington-Kirkpatrick Model in the Presence of Discrete Random Fields
The infinite-range-interaction Ising spin glass is considered in the presence
of an external random magnetic field following a trimodal (three-peak)
distribution. The model is studied through the replica method and phase
diagrams are obtained within the replica-symmetry approximation. It is shown
that the border of the ferromagnetic phase may present first-order phase
transitions, as well as tricritical points at finite temperatures. Analogous to
what happens for the Ising ferromagnet under a trimodal random field, it is
verified that the first-order phase transitions are directly related to the
dilution in the fields (represented by ). The ferromagnetic boundary at
zero temperature also exhibits an interesting behavior: for , a single tricritical point occurs, whereas if
the critical frontier is completely continuous; however, for
, a fourth-order critical point appears. The stability
analysis of the replica-symmetric solution is performed and the regions of
validity of such a solution are identified; in particular, the Almeida-Thouless
line in the plane field versus temperature is shown to depend on the weight
.Comment: 23pages, 7 ps figure
Ising Spin Glass in a Transverse Magnetic Field
We study the three-dimensional quantum Ising spin glass in a transverse
magnetic field following the evolution of the bond probability distribution
under Renormalisation Group transformations. The phase diagram (critical
temperature {\em vs} transverse field ) we obtain shows a finite
slope near , in contrast with the infinite slope for the pure case. Our
results compare very well with the experimental data recently obtained for the
dipolar Ising spin glass LiHoYF, in a transverse field.
This indicates that this system is more apropriately described by a model with
short range interactions than by an equivalent Sherrington-Kirkpatrick model in
a transverse field.Comment: 7 pages, RevTeX3, Nota Cientifica PUC-Rio 23/9
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