267 research outputs found
Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
We study the non-equilibrium relaxation of the spherical spin-glass model
with p-spin interactions in the limit. We analytically
solve the asymptotics of the magnetization and the correlation and response
functions for long but finite times. Even in the thermodynamic limit the system
exhibits `weak' (as well as `true') ergodicity breaking and aging effects. We
determine a functional Parisi-like order parameter which plays a
similar role for the dynamics to that played by the usual function for the
statics.Comment: 8 pages, Roma preprin
Tensionless structure of glassy phase
We study a class of homogeneous finite-dimensional Ising models which were
recently shown to exhibit glassy properties. Monte Carlo simulations of a
particular three-dimensional model in this class show that the glassy phase
obtained under slow cooling is dominated by large scale excitations whose
energy scales with their size as with
. Simulations suggest that in another model of this class,
namely the four-spin model, energy is concentrated mainly in linear defects
making also in this case domain walls tensionless. Two-dimensinal variants of
these models are trivial and energy of excitations scales with the exponent
.Comment: 5 page
The Chiral Phase Transition in Dissipative Dynamics
Numerical simulations of the chiral phase transition in the (3+1)dimensional
O(4)-model are presented. The evolutions of the chiral field follow purely
dissipative dynamics, starting from random chirally symmetric initial
configurations down to the true vacuum with spontaneously broken symmetry. The
model stabilizes topological textures which are formed together with domains of
disoriented chiral condensate (DCC) during the roll-down phase. The classically
evolving field acts as source for the emission of pions and mesons.
The exponents of power laws for the growth of angular correlations and for
emission rates are extracted. Fluctuations in the abundance ratios for neutral
and charged pions are compared with those for uncorrelated sources as potential
signature for the chiral phase transition after heavy-ion collisions. It is
found that the presence of stabilizing textures (baryons and antibaryons)
prevents sufficiently rapid growth of DCC-domain size, so observability of
anomalous tails in the abundance ratios is unlikely. However, the transient
formation of growing DCC domains causes sizable broadening of the distributions
as compared to the statistical widths of generic sources.Comment: 28 pages, 8 figure
Reaction Diffusion Models in One Dimension with Disorder
We study a large class of 1D reaction diffusion models with quenched disorder
using a real space renormalization group method (RSRG) which yields exact
results at large time. Particles (e.g. of several species) undergo diffusion
with random local bias (Sinai model) and react upon meeting. We obtain the
large time decay of the density of each specie, their associated universal
amplitudes, and the spatial distribution of particles. We also derive the
spectrum of exponents which characterize the convergence towards the asymptotic
states. For reactions with several asymptotic states, we analyze the dynamical
phase diagram and obtain the critical exponents at the transitions. We also
study persistence properties for single particles and for patterns. We compute
the decay exponents for the probability of no crossing of a given point by,
respectively, the single particle trajectories () or the thermally
averaged packets (). The generalized persistence exponents
associated to n crossings are also obtained. Specifying to the process or A with probabilities , we compute exactly the exponents
and characterizing the survival up to time t of a domain
without any merging or with mergings respectively, and and
characterizing the survival up to time t of a particle A without
any coalescence or with coalescences respectively.
obey hypergeometric equations and are numerically surprisingly close to pure
system exponents (though associated to a completely different diffusion
length). Additional disorder in the reaction rates, as well as some open
questions, are also discussed.Comment: 54 pages, Late
Possible Localized Modes in the Uniform Quantum Heisenberg Chains of Sr2CuO3
A model of mobile-bond defects is tentatively proposed to analyze the
"anomalies" observed on the NMR spectrum of the quantum Heisenberg chains of
Sr2CuO3. A bond-defect is a local change in the exchange coupling. It results
in a local alternating magnetization (LAM), which when the defect moves,
creates a flipping process of the local field seen by each nuclear spin. At low
temperature, when the overlap of the LAM becomes large, the defects form a
periodic structure, which extends over almost all the chains. In that regime,
the density of bond-defects decreases linearly with T.Comment: 4 pages + 3 figures. To appear in Physical Review
Scaling properties in off equilibrium dynamical processes
In the present paper, we analyze the consequences of scaling hypotheses on
dynamic functions, as two times correlations . We show, under general
conditions, that must obey the following scaling behavior , where the scaling variable is
and , two
undetermined functions. The presence of a non constant exponent
signals the appearance of multiscaling properties in the dynamics.Comment: 6 pages, no figure
DCC Dynamics in (2+1)D-O(3) model
The dynamics of symmetry-breaking after a quench is numerically simulated on
a lattice for the (2+1)-dimensional O(3) model. In addition to the standard
sigma-model with temperature-dependent Phi^4-potential the energy functional
includes a four-derivative current-current coupling to stabilize the size of
the emerging extended topological textures. The total winding number can be
conserved by constraint. As a model for the chiral phase transition during the
cooling phase after a hadronic collision this allows to investigate the
interference of 'baryon-antibaryon' production with the developing disoriented
aligned domains. The growth of angular correlations, condensate, average
orientation is studied in dependence of texture size, quench rate, symmetry
breaking. The classical dissipative dynamics determines the rate of energy
emitted from the relaxing source for each component of the 3-vector field which
provides a possible signature for domains of Disoriented Chiral Condensate. We
find that the 'pions' are emitted in two distinct pulses; for sufficiently
small lattice size the second one carries the DCC signal, but it is strongly
suppressed as compared to simultaneous 'sigma'-meson emission. We compare the
resulting anomalies in the distributions of DCC pions with probabilities
derived within the commonly used coherent state formalism.Comment: 27 pages, 17 figures; several minor insertions in the text; two
references adde
Revival of the spin-Peierls transition in Cu_xZn_(1-x)GeO_3 under pressure
Pressure and temperature dependent susceptibility and Raman scattering
experiments on single crystalline Cu_xZn_(1-x)GeO_3 have shown an unusually
strong increase of the spin-Peierls phase transition temperature upon applying
hydrostatic pressure. The large positive pressure coefficient (7.5 K/GPa) -
almost twice as large as for the pure compound (4.5 K/GPa) - is interpreted as
arising due to an increasing magnetic frustration which decreases the spin-spin
correlation length, and thereby weakens the influence of the non-magnetic
Zn-substitution.Comment: LaTeX, 15 pages, 5 eps figures, Phys. Rev. B, to appea
The nature of slow dynamics in a minimal model of frustration-limited domains
We present simulation results for the dynamics of a schematic model based on
the frustration-limited domain picture of glass-forming liquids. These results
are compared with approximate theoretical predictions analogous to those
commonly used for supercooled liquid dynamics. Although model relaxation times
increase by several orders of magnitude in a non-Arrhenius manner as a
microphase separation transition is approached, the slow relaxation is in many
ways dissimilar to that of a liquid. In particular, structural relaxation is
nearly exponential in time at each wave vector, indicating that the mode
coupling effects dominating liquid relaxation are comparatively weak within
this model. Relaxation properties of the model are instead well reproduced by
the simplest dynamical extension of a static Hartree approximation. This
approach is qualitatively accurate even for temperatures at which the mode
coupling approximation predicts loss of ergodicity. These results suggest that
the thermodynamically disordered phase of such a minimal model poorly
caricatures the slow dynamics of a liquid near its glass transition
Crystallization of a supercooled liquid and of a glass - Ising model approach
Using Monte Carlo simulations we study crystallization in the
three-dimensional Ising model with four-spin interaction. We monitor the
morphology of crystals which grow after placing crystallization seeds in a
supercooled liquid. Defects in such crystals constitute an intricate and very
stable network which separate various domains by tensionless domain walls. We
also show that the crystallization which occurs during the continuous heating
of the glassy phase takes place at a heating-rate dependent temperature.Comment: 7 page
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