Vison gap in the Rokhsar-Kivelson dimer model on the triangular lattice

With the classical Monte Carlo method, I find the energy gap in the Rokhsar-Kivelson dimer model on the triangular lattice. I identify the lowest excitations as visons, and compute their energy as a function of the momentum.Comment: 5 page

MCA: Multiresolution Correlation Analysis, a graphical tool for subpopulation identification in single-cell gene expression data

Background: Biological data often originate from samples containing mixtures of subpopulations, corresponding e.g. to distinct cellular phenotypes. However, identification of distinct subpopulations may be difficult if biological measurements yield distributions that are not easily separable. Results: We present Multiresolution Correlation Analysis (MCA), a method for visually identifying subpopulations based on the local pairwise correlation between covariates, without needing to define an a priori interaction scale. We demonstrate that MCA facilitates the identification of differentially regulated subpopulations in simulated data from a small gene regulatory network, followed by application to previously published single-cell qPCR data from mouse embryonic stem cells. We show that MCA recovers previously identified subpopulations, provides additional insight into the underlying correlation structure, reveals potentially spurious compartmentalizations, and provides insight into novel subpopulations. Conclusions: MCA is a useful method for the identification of subpopulations in low-dimensional expression data, as emerging from qPCR or FACS measurements. With MCA it is possible to investigate the robustness of covariate correlations with respect subpopulations, graphically identify outliers, and identify factors contributing to differential regulation between pairs of covariates. MCA thus provides a framework for investigation of expression correlations for genes of interests and biological hypothesis generation.Comment: BioVis 2014 conferenc

Some generic aspects of bosonic excitations in disordered systems

We consider non-interacting bosonic excitations in disordered systems, emphasising generic features of quadratic Hamiltonians in the absence of Goldstone modes. We discuss relationships between such Hamiltonians and the symmetry classes established for fermionic systems. We examine the density \rho(\omega) of excitation frequencies \omega, showing how the universal behavior \rho(\omega) ~ \omega^4 for small \omega can be obtained both from general arguments and by detailed calculations for one-dimensional models

Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions

The Kardar-Parisi-Zhang (KPZ) equation with infinitesimal surface tension, dynamically develops sharply connected valley structures within which the height derivative is not continuous. We discuss the intermittency issue in the problem of stationary state forced KPZ equation in 1+1--dimensions. It is proved that the moments of height increments $C_a =$ behave as $|x_1 -x_2|^{\xi_a}$ with $\xi_a = a$ for length scales $|x_1-x_2| << \sigma$. The length scale $\sigma$ is the characteristic length of the forcing term. We have checked the analytical results by direct numerical simulation.Comment: 13 pages, 9 figure

Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?

The motion of driven interfaces in random media at finite temperature $T$ and small external force $F$ is usually described by a linear displacement $h_G(t) \sim V(F,T) t$ at large times, where the velocity vanishes according to the creep formula as $V(F,T) \sim e^{-K(T)/F^{\mu}}$ for $F \to 0$. In this paper, we question this picture on the specific example of the directed polymer in a two dimensional random medium. We have recently shown (C. Monthus and T. Garel, arxiv:0802.2502) that its dynamics for F=0 can be analyzed in terms of a strong disorder renormalization procedure, where the distribution of renormalized barriers flows towards some "infinite disorder fixed point". In the present paper, we obtain that for small $F$, this "infinite disorder fixed point" becomes a "strong disorder fixed point" with an exponential distribution of renormalized barriers. The corresponding distribution of trapping times then only decays as a power-law $P(\tau) \sim 1/\tau^{1+\alpha}$, where the exponent $\alpha(F,T)$ vanishes as $\alpha(F,T) \propto F^{\mu}$ as $F \to 0$. Our conclusion is that in the small force region $\alpha(F,T)<1$, the divergence of the averaged trapping time $\bar{\tau}=+\infty$ induces strong non-self-averaging effects that invalidate the usual creep formula obtained by replacing all trapping times by the typical value. We find instead that the motion is only sub-linearly in time $h_G(t) \sim t^{\alpha(F,T)}$, i.e. the asymptotic velocity vanishes V=0. This analysis is confirmed by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape. We moreover obtain that the roughness exponent, which is governed by the equilibrium value $\zeta_{eq}=2/3$ up to some large scale, becomes equal to $\zeta=1$ at the largest scales.Comment: v3=final versio

Possible Glassiness in a Periodic Long-Range Josephson Array

We present an analytic study of a periodic Josephson array with long-range interactions in a transverse magnetic field. We find that this system exhibits a first-order transition into a phase characterized by an extensive number of states separated by barriers that scale with the system size; the associated discontinuity is small in the limit of weak applied field, thus permitting an explicit analysis in this regime.Comment: 4 pages, 2 Postscript figures in a separate file

Replica symmetry breaking in long-range glass models without quenched disorder

We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The formalism is applied to the long range Ising model with orthogonal coupling matrix. We find the one step replica-symmetry breaking solution and show that it is stable in the intermediate temperature range that includes the glass state but excludes very low temperatures. At very low temperatures this solution becomes unstable and this approach fails.Comment: 6 pages, 2 figure

On the theory of diamagnetism in granular superconductors

We study a highly disordered network of superconducting granules linked by weak Josephson junctions in magnetic field and develop a mean field theory for this problem. The diamagnetic response to a slow {\it variations} of magnetic field is found to be analogous to the response of a type-II superconductor with extremely strong pinning. We calculate an effective penetration depth $\lambda_g$ and critical current $j_c$ and find that both $\lambda_g^{-1}$ and $j_c$ are non-zero but are strongly suppressed by frustration.Comment: REVTEX, 12 pages, two Postscript figure

Elastic Theory of pinned flux lattices

The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to $O(\epsilon=4-d)$, the functional renormalization group. We find universal logarithmic growth of displacements for $2<d<4$: $\overline{\langle u(x)-u(0) \rangle ^2}\sim A_d \log|x|$ and persistence of algebraic quasi-long range translational order. When the two methods can be compared they agree within $10\%$ on the value of $A_d$. We compute the function describing the crossover between the ``random manifold'' regime and the logarithmic regime. This crossover should be observable in present decoration experiments.Comment: 12 pages, Revtex 3.

Glassy behaviour in disordered systems with non-relaxational dynamics

We show that a family of disordered systems with non-relaxational dynamics may exhibit ``glassy'' behavior at nonzero temperature, although such a behavior appears to be ruled out by a face-value application of mean-field theory. Nevertheless, the roots of this behavior can be understood within mean-field theory itself, properly interpreted. Finite systems belonging to this family have a dynamical regime with a self-similar pattern of alternating periods of fast motion and trapping.Comment: 4 pages, 4 figure