Finite-size scaling properties of random transverse-field Ising chains : Comparison between canonical and microcanonical ensembles for the disorder

The Random Transverse Field Ising Chain is the simplest disordered model presenting a quantum phase transition at T=0. We compare analytically its finite-size scaling properties in two different ensembles for the disorder (i) the canonical ensemble, where the disorder variables are independent (ii) the microcanonical ensemble, where there exists a global constraint on the disorder variables. The observables under study are the surface magnetization, the correlation of the two surface magnetizations, the gap and the end-to-end spin-spin correlation $C(L)$ for a chain of length $L$. At criticality, each observable decays typically as $e^{- w \sqrt{L}}$ in both ensembles, but the probability distributions of the rescaled variable $w$ are different in the two ensembles, in particular in their asymptotic behaviors. As a consequence, the dependence in $L$ of averaged observables differ in the two ensembles. For instance, the correlation $C(L)$ decays algebraically as 1/L in the canonical ensemble, but sub-exponentially as $e^{-c L^{1/3}}$ in the microcanonical ensemble. Off criticality, probability distributions of rescaled variables are governed by the critical exponent $\nu=2$ in both ensembles, but the following observables are governed by the exponent $\tilde \nu=1$ in the microcanonical ensemble, instead of the exponent $\nu=2$ in the canonical ensemble (a) in the disordered phase : the averaged surface magnetization, the averaged correlation of the two surface magnetizations and the averaged end-to-end spin-spin correlation (b) in the ordered phase : the averaged gap. In conclusion, the measure of the rare events that dominate various averaged observables can be very sensitive to the microcanonical constraint.Comment: 24 page

Feedback-control of quantum systems using continuous state-estimation

We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. Direct feedback may be combined with feedback by estimation, and the resulting combination, performed on a linear system, is closely analogous to classical LQG control theory with residual feedback.Comment: 12 pages, multicol revtex, revised and extende

Dynamics of Gravity in a Higgs Phase

We investigate the universal low-energy dynamics of the simplest Higgs phase for gravity, `ghost condensation.' We show that the nonlinear dynamics of the `ghostone' field dominate for all interesting gravitational sources. Away from caustic singularities, the dynamics is equivalent to the irrotational flow of a perfect fluid with equation of state p \propto \rho^2, where the fluid particles can have negative mass. We argue that this theory is free from catastrophic instabilities due to growing modes, even though the null energy condition is violated. Numerical simulations show that solutions generally have singularities in which negative energy regions shrink to zero size. We exhibit partial UV completions of the theory in which these singularities are smoothly resolved, so this does not signal any inconsistency in the effective theory. We also consider the bounds on the symmetry breaking scale M in this theory. We argue that the nonlinear dynamics cuts off the Jeans instability of the linear theory, and allows M \lsim 100MeV.Comment: 54 pages, 15 figures; postscript figures downloadable from http://schwinger.harvard.edu/~wiseman/Ghost/ghostepsfigs.tar.gz ; v2: substantial revision to section 5 on bound

On the critical behavior of disordered quantum magnets: The relevance of rare regions

The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered non-perturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.Comment: 16 pp., REVTeX, epsf, 2 figs, final version as publishe

Smeared phase transition in a three-dimensional Ising model with planar defects: Monte-Carlo simulations

We present results of large-scale Monte Carlo simulations for a three-dimensional Ising model with short range interactions and planar defects, i.e., disorder perfectly correlated in two dimensions. We show that the phase transition in this system is smeared, i.e., there is no single critical temperature, but different parts of the system order at different temperatures. This is caused by effects similar to but stronger than Griffiths phenomena. In an infinite-size sample there is an exponentially small but finite probability to find an arbitrary large region devoid of impurities. Such a rare region can develop true long-range order while the bulk system is still in the disordered phase. We compute the thermodynamic magnetization and its finite-size effects, the local magnetization, and the probability distribution of the ordering temperatures for different samples. Our Monte-Carlo results are in good agreement with a recent theory based on extremal statistics.Comment: 9 pages, 6 eps figures, final version as publishe

Crossover and self-averaging in the two-dimensional site-diluted Ising model

Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent $T_c(L)$ and the sample average of physical quantities at each $T_c(L)$ systematically. Using the finite-size scaling (FSS) analysis for $T_c(L)$, we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature $T_c(L)$. Its variance shows the power-law $L$ dependence, $L^{-n}$, and the estimate of the exponent $n$ is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. {\bf 77}, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent $T_c(L)$, we show that the 2D site-diluted Ising model exhibits weak self-averaging.Comment: 6 pages including 6 eps figures, RevTeX, to appear in Phys. Rev.

Random walks and polymers in the presence of quenched disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

Scaling and finte-size-scaling in the two dimensional random-coupling Ising ferromagnet

It is shown by Monte Carlo method that the finite size scaling (FSS) holds in the two dimensional random-coupled Ising ferromagnet. It is also demonstrated that the form of universal FSS function constructed via novel FSS scheme depends on the strength of the random coupling for strongly disordered cases. Monte Carlo measurements of thermodynamic (infinite volume limit) data of the correlation length ($\xi$) up to $\xi \simeq 200$ along with measurements of the fourth order cumulant ratio (Binder's ratio) at criticality are reported and analyzed in view of two competing scenarios. It is demonstrated that the data are almost exclusively consistent with the scenario of weak universality.Comment: 9 pages, 4figuer

Untangling the effects of overexploration and overexploitation on organizational performance: The moderating role of environmental dynamism

Because a firm's optimal knowledge search behavior is determined by unique firm and industry conditions, organizational performance should be contingent oil the degree to which a firm's actual level of knowledge search deviates from the optimal level. It is thus hypothesized that deviation from the optimal search, in the form of either overexploitation or overexploration, is detrimental to organizational performance. Furthermore, the negative effect of search deviation oil organizational performance varies with environmental dynamism: that is, overexploitation is expected to become more harmful. whereas overexploration becomes less so with all increase in environmental dynamism. The empirical analyses yield results consistent with these arguments. Implications for research and practice are correspondingly discussed