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 $N \rightarrow \infty$ 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 $P_d(q)$ 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 $E_l$ scales with their size $l$ as $E_l\sim l^{\Theta}$ with $\Theta\sim 1.33(5)$. 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 $\Theta=1.05(5)$.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 $\sigma$ 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 ($\theta$) or the thermally averaged packets ($\bar{\theta}$). The generalized persistence exponents associated to n crossings are also obtained. Specifying to the process $A+A \to \emptyset$ or A with probabilities $(r,1-r)$, we compute exactly the exponents $\delta(r)$ and $\psi(r)$ characterizing the survival up to time t of a domain without any merging or with mergings respectively, and $\delta_A(r)$ and $\psi_A(r)$ characterizing the survival up to time t of a particle A without any coalescence or with coalescences respectively. $\bar{\theta}, \psi, \delta$ 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 $C(t,t')$. We show, under general conditions, that $C(t,t')$ must obey the following scaling behavior $C(t,t') = \phi_1(t)^{f(\beta)}{\cal{S}}(\beta)$, where the scaling variable is $\beta=\beta(\phi_1(t')/\phi_1(t))$ and $\phi_1(t')$, $\phi_1(t)$ two undetermined functions. The presence of a non constant exponent $f(\beta)$ 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