Phase Ordering of 2D XY Systems Below T_{KT}

We consider quenches in non-conserved two-dimensional XY systems between any two temperatures below the Kosterlitz-Thouless transition. The evolving systems are defect free at coarse-grained scales, and can be exactly treated. Correlations scale with a characteristic length $L(t) \propto t^{1/2}$ at late times. The autocorrelation decay exponent, $\bar{\lambda} = (\eta_i+\eta_f)/2$, depends on both the initial and the final state of the quench through the respective decay exponents of equilibrium correlations, $C_{EQ}(r) \sim r^{-\eta}$. We also discuss time-dependent quenches.Comment: LATeX 11 pages (REVTeX macros), no figure

Phase Ordering Kinetics with External Fields and Biased Initial Conditions

The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical approach, based on a `gaussian closure' scheme, is developed, and results are obtained for the time-dependence of the mean order parameter, the pair correlation function, the autocorrelation function, and the density of topological defects [e.g. domain walls ($n=1$), or vortices ($n=2$)]. The results are in qualitative agreement with experiments on nematic films and related numerical simulations on the two-dimensional XY model with biased initial conditions.Comment: 35 pages, latex, no figure

Response of non-equilibrium systems with long-range initial correlations

The long-time dynamics of the $d$-dimensional spherical model with a non-conserved order parameter and quenched from an initial state with long-range correlations is studied through the exact calculation of the two-time autocorrelation and autoresponse functions. In the aging regime, these are given in terms of non-trivial universal scaling functions of both time variables. At criticality, five distinct types of aging are found, depending on the form of the initial correlations, while at low temperatures only a single type of aging exists. The autocorrelation and autoreponse exponents are shown to be generically different and to depend on the initial conditions. The scaling form of the two-time response functions agrees with a recent prediction coming from local scale invariance.Comment: Latex, 18pp, 2 figures (final version

Mean Field Theory of Josephson Junction Arrays with Charge Frustration

Using the path integral approach, we provide an explicit derivation of the equation for the phase boundary for quantum Josephson junction arrays with offset charges and non-diagonal capacitance matrix. For the model with nearest neighbor capacitance matrix and uniform offset charge $q/2e=1/2$, we determine, in the low critical temperature expansion, the most relevant contributions to the equation for the phase boundary. We explicitly construct the charge distributions on the lattice corresponding to the lowest energies. We find a reentrant behavior even with a short ranged interaction. A merit of the path integral approach is that it allows to provide an elegant derivation of the Ginzburg-Landau free energy for a general model with charge frustration and non-diagonal capacitance matrix. The partition function factorizes as a product of a topological term, depending only on a set of integers, and a non-topological one, which is explicitly evaluated.Comment: LaTex, 24 pages, 8 figure

Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?

We study spatio-temporal fluctuations in the non-equilibrium dynamics of the d dimensional O(N) in the large N limit. We analyse the invariance of the dynamic equations for the global correlation and response in the slow ageing regime under transformations of time. We find that these equations are invariant under scale transformations. We extend this study to the action in the dynamic generating functional finding similar results. This model therefore falls into a different category from glassy problems in which full time-reparametrisation invariance, a larger symmetry that emcompasses time scale invariance, is expected to be realised asymptotically. Consequently, the spatio-temporal fluctuations of the large N O(N) model should follow a different pattern from that of glassy systems. We compute the fluctuations of local, as well as spatially separated, two-field composite operators and responses, and we confront our results with the ones found numerically for the 3d Edwards-Anderson model and kinetically constrained lattice gases. We analyse the dependence of the fluctuations of the composite operators on the growing domain length and we compare to what has been found in super-cooled liquids and glasses. Finally, we show that the development of time-reparametrisation invariance in glassy systems is intimately related to a well-defined and finite effective temperature, specified from the modification of the fluctuation-dissipation theorem out of equilibrium. We then conjecture that the global asymptotic time-reparametrisation invariance is broken down to time scale invariance in all coarsening systems.Comment: 57 pages, 5 figure

The Energy-Scaling Approach to Phase-Ordering Growth Laws

We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on a scaling assumption for pair correlations, determines $L(t)$ self-consistently for purely dissipative dynamics by computing the time-dependence of the energy in two ways. We derive growth laws for conserved and non-conserved $O(n)$ models, including two-dimensional XY models and systems with textures. We demonstrate that the growth laws for other systems, such as liquid-crystals and Potts models, are determined by the type of topological defect in the order parameter field that dominates the energy. We also obtain generalized Porod laws for systems with topological textures.Comment: LATeX 18 pages (REVTeX macros), one postscript figure appended, REVISED --- rearranged and clarified, new paragraph on naive dimensional analysis at end of section I

Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions

We have studied a quantum Hamiltonian that models an array of ultrasmall Josephson junctions with short range Josephson couplings, $E_J$, and charging energies, $E_C$, due to the small capacitance of the junctions. We derive a new effective quantum spherical model for the array Hamiltonian. As an application we start by approximating the capacitance matrix by its self-capacitive limit and in the presence of an external uniform background of charges, $q_x$. In this limit we obtain the zero-temperature superconductor-insulator phase diagram, $E_J^{\rm crit}(E_C,q_x)$, that improves upon previous theoretical results that used a mean field theory approximation. Next we obtain a closed-form expression for the conductivity of a square array, and derive a universal scaling relation valid about the zero--temperature quantum critical point. In the latter regime the energy scale is determined by temperature and we establish universal scaling forms for the frequency dependence of the conductivity.Comment: 18 pages, four Postscript figures, REVTEX style, Physical Review B 1999. We have added one important reference to this version of the pape

Quantum-Phase Transitions of Interacting Bosons and the Supersolid Phase

We investigate the properties of strongly interacting bosons in two dimensions at zero temperature using mean-field theory, a variational Ansatz for the ground state wave function, and Monte Carlo methods. With on-site and short-range interactions a rich phase diagram is obtained. Apart from the homogeneous superfluid and Mott-insulating phases, inhomogeneous charge-density wave phases appear, that are stabilized by the finite-range interaction. Furthermore, our analysis demonstrates the existence of a supersolid phase, in which both long-range order (related to the charge-density wave) and off-diagonal long-range order coexist. We also obtain the critical exponents for the various phase transitions.Comment: RevTex, 20 pages, 10 PostScript figures include

The kinetic spherical model in a magnetic field

The long-time kinetics of the spherical model in an external magnetic field and below the equilibrium critical temperature is studied. The solution of the associated stochastic Langevin equation is reduced exactly to a single non-linear Volterra equation. For a sufficiently small external field, the kinetics of the magnetization-reversal transition from the metastable to the ground state is compared to the ageing behaviour of coarsening systems quenched into the low-temperature phase. For an oscillating magnetic field and below the critical temperature, we find evidence for the absence of the frequency-dependent dynamic phase transition, which was observed previously to occur in Ising-like systems.Comment: 26 pages, 12 figure

Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics

We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal parts yields a closed exact RG equation for the local part, to a given order in the local part. The method is illustrated on the O(N) model by straightforwardly recovering the $\eta$ exponent and scaling functions. Then it is applied to study the glass phase of the Cardy-Ostlund, random phase sine Gordon model near the glass transition temperature. The static correlations and equilibrium dynamical exponent $z$ are recovered and several new results are obtained. The equilibrium two-point scaling functions are obtained. The nonequilibrium, finite momentum, two-time $t,t'$ response and correlations are computed. They are shown to exhibit scaling forms, characterized by novel exponents $\lambda_R \neq \lambda_C$, as well as universal scaling functions that we compute. The fluctuation dissipation ratio is found to be non trivial and of the form $X(q^z (t-t'), t/t')$. Analogies and differences with pure critical models are discussed.Comment: 33 pages, RevTe