Glass and polycrystal states in a lattice spin model

We numerically study a nondisordered lattice spin system with a first order liquid-crystal transition, as a model for supercooled liquids and glasses. Below the melting temperature the system can be kept in the metastable liquid phase, and it displays a dynamic phenomenology analogous to fragile supercooled liquids, with stretched exponential relaxation, power law increase of the relaxation time and high fragility index. At an effective spinodal temperature Tsp the relaxation time exceeds the crystal nucleation time, and the supercooled liquid loses stability. Below Tsp liquid properties cannot be extrapolated, in line with Kauzmann's scenario of a `lower metastability limit' of supercooled liquids as a solution of Kauzmann's paradox. The off-equilibrium dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal droplets, followed by extremely slow growth, due to the presence of pinning energy barriers. In the early time region, which is longer the lower the temperature, this crystal-growth phase is indistinguishable from an off-equilibrium glass, both from a structural and a dynamical point of view: crystal growth has not advanced enough to be structurally detectable, and a violation of the fluctuation-dissipation theorem (FDT) typical of structural glasses is observed. On the other hand, for longer times crystallization reaches a threshold beyond which crystal domains are easily identified, and FDT violation becomes compatible with ordinary domain growth.Comment: 25 page

Statistics of energy levels and zero temperature dynamics for deterministic spin models with glassy behaviour

We consider the zero-temperature dynamics for the infinite-range, non translation invariant one-dimensional spin model introduced by Marinari, Parisi and Ritort to generate glassy behaviour out of a deterministic interaction. It is shown that there can be a large number of metatastable (i.e., one-flip stable) states with very small overlap with the ground state but very close in energy to it, and that their total number increases exponentially with the size of the system.Comment: 25 pages, 8 figure

Energy Landscape Statistics of the Random Orthogonal Model

The Random Orthogonal Model (ROM) of Marinari-Parisi-Ritort [MPR1,MPR2] is a model of statistical mechanics where the couplings among the spins are defined by a matrix chosen randomly within the orthogonal ensemble. It reproduces the most relevant properties of the Parisi solution of the Sherrington-Kirckpatrick model. Here we compute the energy distribution, and work out an extimate for the two-point correlation function. Moreover, we show exponential increase of the number of metastable states also for non zero magnetic field.Comment: 23 pages, 6 figures, submitted to J. Phys.

Thermodynamical Limit for Correlated Gaussian Random Energy Models

Let \{E_{\s}(N)\}_{\s\in\Sigma_N} be a family of $|\Sigma_N|=2^N$ centered unit Gaussian random variables defined by the covariance matrix $C_N$ of elements \displaystyle c_N(\s,\tau):=\av{E_{\s}(N)E_{\tau}(N)}, and H_N(\s) = - \sqrt{N} E_{\s}(N) the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition $N=N_1+N_2$, and all pairs (\s,\t)\in \Sigma_N\times \Sigma_N: c_N(\s,\tau)\leq \frac{N_1}{N} c_{N_1}(\pi_1(\s),\pi_1(\tau))+ \frac{N_2}{N} c_{N_2}(\pi_2(\s),\pi_2(\tau)) where \pi_k(\s), k=1,2 are the projections of \s\in\Sigma_N into $\Sigma_{N_k}$. The condition is explicitly verified for the Sherrington-Kirckpatrick, the even $p$-spin, the Derrida REM and the Derrida-Gardner GREM models.Comment: 15 pages, few remarks and two references added. To appear in Commun. Math. Phy

A phase-separation perspective on dynamic heterogeneities in glass-forming liquids

We study dynamic heterogeneities in a model glass-former whose overlap with a reference configuration is constrained to a fixed value. The system phase-separates into regions of small and large overlap, so that dynamical correlations remain strong even for asymptotic times. We calculate an appropriate thermodynamic potential and find evidence of a Maxwell's construction consistent with a spinodal decomposition of two phases. Our results suggest that dynamic heterogeneities are the expression of an ephemeral phase-separating regime ruled by a finite surface tension

Glassy dynamics, metastability limit and crystal growth in a lattice spin model

We introduce a lattice spin model where frustration is due to multibody interactions rather than quenched disorder in the Hamiltonian. The system has a crystalline ground state and below the melting temperature displays a dynamic behaviour typical of fragile glasses. However, the supercooled phase loses stability at an effective spinodal temperature, and thanks to this the Kauzmann paradox is resolved. Below the spinodal the system enters an off-equilibrium regime corresponding to fast crystal nucleation followed by slow activated crystal growth. In this phase and in a time region which is longer the lower the temperature we observe a violation of the fluctuation-dissipation theorem analogous to structural glasses. Moreover, we show that in this system there is no qualitative difference between a locally stable glassy configuration and a highly disordered polycrystal

Silent Flocks

Experiments find coherent information transfer through biological groups on length and time scales distinctly below those on which asymptotically correct hydrodynamic theories apply. We present here a new continuum theory of collective motion coupling the velocity and density fields of Toner and Tu to the inertial spin field recently introduced to describe information propagation in natural flocks of birds. The long-wavelength limit of the new equations reproduces Toner-Tu theory, while at shorter wavelengths (or, equivalently, smaller damping), spin fluctuations dominate over density fluctuations and second sound propagation of the kind observed in real flocks emerges. We study the dispersion relation of the new theory and find that when the speed of second sound is large, a gap sharply separates first from second sound modes. This gap implies the existence of `silent' flocks, namely medium-sized systems across which neither first nor second sound can propagate

Quasifission and fusion-fission in massive nuclei reactions. Comparison of reactions leading to the Z=120 element

The yields of evaporation residues, fusion-fission and quasifission fragments in the $^{48}$Ca+$^{144,154}$Sm and $^{16}$O+$^{186}$W reactions are analyzed in the framework of the combined theoretical method based on the dinuclear system concept and advanced statistical model. The measured yields of evaporation residues for the $^{48}$Ca+$^{154}$Sm reaction can be well reproduced. The measured yields of fission fragments are decomposed into contributions coming from fusion-fission, quasifission, and fast-fission. The decrease in the measured yield of quasifission fragments in $^{48}$Ca+$^{154}$Sm at the large collision energies and the lack of quasifission fragments in the $^{48}$Ca+$^{144}$Sm reaction are explained by the overlap in mass-angle distributions of the quasifission and fusion-fission fragments. The investigation of the optimal conditions for the synthesis of the new element $Z$=120 ($A$=302) show that the $^{54}$Cr+$^{248}$Cm reaction is preferable in comparison with the $^{58}$Fe+$^{244}$Pu and $^{64}$Ni+$^{238}$U reactions because the excitation function of the evaporation residues of the former reaction is some orders of magnitude larger than that for the last two reactions.Comment: 27 pages, 12 figures, submitted to Phys. Rev.

Off-equilibrium confined dynamics in a glassy system with level-crossing states

We study analytically the dynamics of a generalized p-spin model, starting with a thermalized initial condition. The model presents birth and death of states, hence the dynamics (even starting at equilibrium) may go out of equilibrium when the temperature is varied. We give a full description of this constrained out of equilibrium behavior and we clarify the connection to the thermodynamics by computing (sub-dominant) TAP states, constrained to the starting equilibrium configuration.Comment: 10 pages, 3 figures; longer version with appendi