Random and aperiodic quantum spin chains: A comparative study

According to the Harris-Luck criterion the relevance of a fluctuating interaction at the critical point is connected to the value of the fluctuation exponent omega. Here we consider different types of relevant fluctuations in the quantum Ising chain and investigate the universality class of the models. At the critical point the random and aperiodic systems behave similarly, due to the same type of extreme broad distribution of the energy scales at low energies. The critical exponents of some averaged quantities are found to be a universal function of omega, but some others do depend on other parameters of the distribution of the couplings. In the off-critical region there is an important difference between the two systems: there are no Griffiths singularities in aperiodic models.Comment: 4 pages RevTeX, 2 eps-figures include

Comparative study of the critical behavior in one-dimensional random and aperiodic environments

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents omega>0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as t ~ log^{1/omega}. Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of omega, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities.Comment: 13 pages RevTeX, 10 eps-figures include

Three-dimensional flows in slowly-varying planar geometries

We consider laminar flow in channels constrained geometrically to remain between two parallel planes; this geometry is typical of microchannels obtained with a single step by current microfabrication techniques. For pressure-driven Stokes flow in this geometry and assuming that the channel dimensions change slowly in the streamwise direction, we show that the velocity component perpendicular to the constraint plane cannot be zero unless the channel has both constant curvature and constant cross-sectional width. This result implies that it is, in principle, possible to design "planar mixers", i.e. passive mixers for channels that are constrained to lie in a flat layer using only streamwise variations of their in-plane dimensions. Numerical results are presented for the case of a channel with sinusoidally varying width

Path integral Monte Carlo study of the interacting quantum double-well model: Quantum phase transition and phase diagram

The discrete time path integral Monte Carlo (PIMC) with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action for a single particle in a double well potential is used to construct the many-particle action. The algorithm is applied to the interacting quantum double-well chain for which the zero-temperature phase diagram is determined. The quantum phase transition is studied via finite-size scaling and the critical exponents are shown to be compatible with the classical two-dimensional (2D) Ising universality class -- not only in the order-disorder limit (deep potential wells) but also in the displacive regime (shallow potential wells).Comment: 17 pages, 7 figures; Accepted for publication in Phys. Rev.

Critical Exponents of the Three Dimensional Random Field Ising Model

The phase transition of the three--dimensional random field Ising model with a discrete ($\pm h$) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific heat, susceptibility, disconnected susceptibility and magnetization are determined simultaneously via finite size scaling. While the exponents for the magnetization and disconnected susceptibility are consistent with a first order transition, the specific heat appears to saturate indicating no latent heat. Sample to sample fluctuations of the susceptibilty are consistent with the droplet picture for the transition.Comment: Revtex, 10 pages + 4 figures included as Latex files and 1 in Postscrip

Fluctuation Dissipation Ratio in Three-Dimensional Spin Glasses

We present an analysis of the data on aging in the three-dimensional Edwards Anderson spin glass model with nearest neighbor interactions, which is well suited for the comparison with a recently developed dynamical mean field theory. We measure the parameter $x(q)$ describing the violation of the relation among correlation and response function implied by the fluctuation dissipation theorem.Comment: LaTeX 10 pages + 4 figures (appended as uuencoded compressed tar-file), THP81-9

Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions

With the help of EXACT ground states obtained by a polynomial algorithm we compute the domain wall energy at zero-temperature for the bond-random and the site-random Ising spin glass model in two dimensions. We find that in both models the stability of the ferromagnetic AND the spin glass order ceases to exist at a UNIQUE concentration p_c for the ferromagnetic bonds. In the vicinity of this critical point, the size and concentration dependency of the first AND second moment of the domain wall energy are, for both models, described by a COMMON finite size scaling form. Moreover, below this concentration the stiffness exponent turns out to be slightly negative \theta_S = -0.056(6) indicating the absence of any intermediate spin glass phase at non-zero temperature.Comment: 7 pages Latex, 5 postscript-figures include

Analysis of within subjects variability in mouse ultrasonic vocalization: Pups exhibit inconsistent, state-like patterns of call production

Mice produce ultrasonic vocalizations (USV) in multiple communicative contexts, including adult social interaction (e.g., male to female courtship), as well as pup calls when separated from the dam. Assessment of pup USV has been widely applied in models of social and communicative disorders, dozens of which have shown alterations to this conserved behavior. However, features such as call production rate can vary substantially even within experimental groups and it is unclear to what extent aspects of USV represent stable trait-like influences or are vulnerable to an animal's state. To address this question, we have employed a mixed modeling approach to describe consistency in USV features across time, leveraging multiple large cohorts recorded from two strains, and across ages/times. We find that most features of pup USV show consistent patterns within a recording session, but inconsistent patterns across postnatal development. This supports the conclusion that pup USV is most strongly influenced by state-like variables. In contrast, adult USV call rate and call duration show higher consistency across sessions and may reflect a stable trait. However, spectral features of adult song such as the presence of pitch jumps do not show this level of consistency, suggesting that pitch modulation is more susceptible to factors affecting the animal's state at the time of recording. Overall, the utility of this work is threefold. First, as variability necessarily affects the sensitivity of the assay to detect experimental perturbation, we hope the information provided here will be used to help researchers plan sufficiently powered experiments, as well as prioritize specific ages to study USV behavior and to decide which features to consider most strongly in analysis. Second, via the mouseTube platform, we have provided these hundreds of recordings and associated data to serve as a shared resource for other researchers interested in either benchmark data for these strains or in developing algorithms for studying features of mouse song. Finally, we hope that this work informs both interpretation of USV studies in models of developmental disorder, and helps to further research into understanding the neural processes that contribute to the production and predictability of USV behavior

Renormalization group study of the two-dimensional random transverse-field Ising model

The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to $L=2048$. We have calculated sample dependent pseudo-critical points and studied their distribution, which is found to be characterized by the same shift and width exponent: $\nu=1.24(2)$. For different types of disorder the infinite disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: $x=0.982(15)$ and $\psi=0.48(2)$. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases