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arXiv2010

Algebraic Topology of Spin Glasses

We study topology of frustration in $d$-dimensional Ising spin glasses with $d\ge 2$ with nearest-neighbor interactions. We prove the following: For any given spin configuration, the domain walls on the unfrustration network are all transverse to a frustrated loop on the unfrustration network, where a domain wall is defined to be a connected element of the collection of all the $(d-1)$-cells which are dual to the bonds having an unfavorable energy, and the unfrustration network is the collection of all the unfrustrated plaquettes. These domain walls are topologically nontrivial because they are all related to the global frustration of a loop on the unfrustration network. Taking account of the thermal stability for the domain walls, we can explain the numerical results that three or higher dimensional systems exhibit a spin glass phase, whereas two-dimensional ones do not. Namely, in two dimensions, the thermal fluctuations of the topologically nontrivial domain walls destroy the order of the frozen spins on the unfrustration network, whereas they do not in three or higher dimensions. This may be interpreted as a global, topological effect of the frustrations.

math-ph↗
arXiv2008

Nature of Structural Transformations in the B2O3 Glass under High Pressure

We report the results of the X-ray diffraction study of B2O3 glass in the pressure interval up to 10 GPa in the 300-700 K temperature range, the results of in-situ volumetric measurements of the glass at pressures up to 9 GPa at room temperature, and first-principles simulations data at pressures up to 250GPa. The behavior of B2O3 glass under pressure can be described as two broad pressure-overlapping transitions. The first transition starts at P > 1 GPa and proceeds without any changes in thecoordination number of the boron atoms; the other one starts at P > 5 GPa and is accompanied by a gradual increase of coordination number. The second transition is completely reversible; the residual densification of the B2O3 glass after decompression is associated with the incomplete reversibility of the first transformation. The fraction of boron atoms transferred to the 4-coordination state in the glass at P < 10 GPa is much smaller than was assumed from indirect experimental data [4], but is considerably larger (by tens of times) than was previously suggested by the classical molecular dynamics simulations [5,6]. The observed transformations under both compression and decompression are quite broad, contrary to the assumption in Ref. [7]. On the basis of ab-initio results, we also predict the one more transformation under higher pressures to a super-dense phase, in which B atoms become 5- and 6-fold coordinated.

cond-mat.dis-nn↗
arXiv2010

Internal Percolation Problem

Introduced and investigated new kind of percolation problem - so called internal percolation problem (IP). In usual percolation problem current flows from top to bottom of the system and here it can be called as external percolation problem (EP) despite of the IP case when voltage is applied to the system through bars which are inside of the hole in system. EP problem has two major parameters: M size of system and a0 size of inclusion, lattice size etc. IP holds one more parameter the size of hole - L. Results of computer simulation show that critical indexes of conductance for IP problem are very close to those in EP problem. In opposite indexes of relative spectral noise density of 1/f noise and higher moments are really differs from EP problem. The source of such behaviour is discussed.

cond-mat.dis-nn↗
arXiv2008

Effect of disorder on the interacting Fermi gases in a one-dimensional optical lattice

Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to an harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.

cond-mat.dis-nn↗
arXiv2008

Statistical Physics of Hard Optimization Problems

Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the NP-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this thesis is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.

cond-mat.stat-mech↗
arXiv2009

Absence of diffusion in certain random lattices: Numerical evidence

We demonstrate, by solving numerically the time-dependent Schroedinger equation, the physical character of electron localization in a disordered two-dimensional lattice. We show, in agreement with the prediction of P. W. Anderson, that the disorder prevents electron diffusion. The electron becomes spatially localized in a specific area of the system. Our numerical analysis confirms that the electron localization is a quantum effect caused by the wave character of electron propagation and has no analogy in classical mechanics.

cond-mat.dis-nn↗
arXiv2008

Exploring the effect of sex on an empirical fitness landscape

The nature of epistasis has important consequences for the evolutionary significance of sex and recombination. Recent efforts to find negative epistasis as source of negative linkage disequilibrium and associated long-term sex advantage have yielded little support. Sign epistasis, where the sign of the fitness effects of alleles varies across genetic backgrounds, is responsible for ruggedness of the fitness landscape with implications for the evolution of sex that have been largely unexplored. Here, we describe fitness landscapes for two sets of strains of the asexual fungus \emph{Aspergillus niger} involving all combinations of five mutations. We find that $\sim 30$% of the single-mutation fitness effects are positive despite their negative effect in the wild-type strain, and that several local fitness maxima and minima are present. We then compare adaptation of sexual and asexual populations on these empirical fitness landscapes using simulations. The results show a general disadvantage of sex on these rugged landscapes, caused by the break down by recombination of genotypes escaping from local peaks. Sex facilitates escape from a local peak only for some parameter values on one landscape, indicating its dependence on the landscape's topography. We discuss possible reasons for the discrepancy between our results and the reports of faster adaptation of sexual populations.

q-bio.PE↗
arXiv2010

Minimum-Free-Energy Distribution of RNA Secondary Structures: Entropic and Thermodynamic Properties of Rare Events

We study the distribution of the minimum free energy (MFE) for the Turner model of pseudoknot free RNA secondary structures over ensembles of random RNA sequences. In particular, we are interested in those rare and intermediate events of unexpected low MFEs. Generalized ensemble Markov-chain Monte Carlo methods allow us to explore the rare-event tail of the MFE distribution down to probabilities like $10^{-70}$ and to study the relationship between the sequence entropy and structural properties for sequence ensembles with fixed MFEs. Entropic and structural properties of those ensembles are compared with natural RNA of the same reduced MFE (z-score).

cond-mat.dis-nn↗
arXiv2008

Maximum memory capacity on neural networks with short-term depression and facilitation

In this work we study, analytically and employing Monte Carlo simulations, the influence of the competition between several activity-dependent synaptic processes, such as short-term synaptic facilitation and depression, on the maximum memory storage capacity in a neural network. In contrast with the case of synaptic depression, which drastically reduces the capacity of the network to store and retrieve "static" activity patterns, synaptic facilitation enhances the storage capacity in different contexts. In particular, we found optimal values of the relevant synaptic parameters (such as the neurotransmitter release probability or the characteristic facilitation time constant) for which the storage capacity can be maximal and similar to the one obtained with static synapses, that is, without activity-dependent processes. We conclude that depressing synapses with a certain level of facilitation allow to recover the good retrieval properties of networks with static synapses while maintaining the nonlinear characteristics of dynamic synapses, convenient for information processing and coding.

q-bio.NC↗
arXiv2009

Exactness of the replica method in perturbation

The replica method for a quenched disordered system is considered in a perturbative field theory. Since correction in a finite-order perturbation is given in a polynomial of the replica number $n$, the zero-replica limit $n \to 0$ is regarded as extracting the constant term from the polynomial, which mathematically makes sense. The meaning of the extraction is clarified comparing with a direct calculation.

cond-mat.dis-nn↗
arXiv2009

Phase diagram, correlation gap, and critical properties of the Coulomb glass

We investigate the lattice Coulomb glass model in three dimensions via Monte Carlo simulations. No evidence for an equilibrium glass phase is found down to very low temperatures, although the correlation length increases rapidly near T=0. A charge-ordered phase (COP) exists at low disorder. The transition to this phase is consistent with the Random Field Ising universality class, which shows that the interaction is effectively screened at moderate temperature. For large disorder, the single-particle density of states near the Coulomb gap satisfies the scaling relation g(e,T)=T^δf(|e|/T) with δ= 2.01 +/- 0.05 in agreement with the prediction of Efros and Shklovskii. For decreasing disorder, a crossover to a larger effective exponent occurs due to the proximity of the COP.

cond-mat.dis-nn↗
arXiv2010

The synchronization transition in correlated oscillator populations

The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators on the network systematically shift the critical point as well as the critical exponents characterizing the transition. Negative correlations imply an onset of synchronization for smaller coupling, whereas positive correlations shift the critical coupling towards larger interaction strengths. For negatively correlated oscillators the transition still exhibits critical behaviour similar to the all-to-all coupled Kuramoto system, while positive correlations change the universality class of the transition depending on the correlation strength. Crucially, the paper demonstrates that the synchronization behaviour is not only determined by the coupling architecture, but is also strongly influenced by the oscillator placement on the coupling network.

cond-mat.stat-mech↗
arXiv2008

Parameter Evaluation of a Simple Mean-Field Model of Social Interaction

The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical and phenomenological point of view. We propose a parameter evaluation procedure and test it by fitting our model against three families of data coming from different cases: the estimated interaction parameters are found to have similar positive values establishing a quantitative confirmation of the peer imitation behavior found in social psychology. Moreover all the values of the interaction parameters belong to the phase transition regime suggesting its possible role in the study of social systems.

physics.soc-ph↗
arXiv2009

Dipole emission and coherent transport in random media I

This is the first of a series of papers devoted to develop a microscopical approach to the dipole emission process and its relation to coherent transport in random media. In this Letter, we deduce general expressions for the decay rate of spontaneous emitters and the power emission of induced dipoles embedded in homogenous dielectric media. We derive formulae which apply generically to virtual cavities and, in the continuum approximation, to small real cavities.

physics.optics↗
arXiv2009

Dipole emission and coherent transport in random media II. Density of states vs. index of refraction

This is the second of a series of papers devoted to develop a microscopical approach to the dipole emission process and its relation to coherent transport in random media. In this Letter, we deduce a relation between the transverse decay rate of an emitter in a virtual cavity and the complex refraction index of the host medium. We argue on the possibility of a criterion for inhibition/enhancement of spontaneous emission in function of the transition frequency and the correlation length of the host scatterers. In addition, we study the radiative/non-radiative nature of the net power emission through a microscopical analysis of the scattering events involved. This study reveals essential discrepancies with previous interpretations.

physics.optics↗
arXiv2008

Glass transitions in 1, 2, 3, and 4 dimensional binary Lennard-Jones systems

We investigate the calorimetric liquid-glass transition by performing simulations of a binary Lennard-Jones mixture in one through four dimensions. Starting at a high temperature, the systems are cooled to T=0 and heated back to the ergodic liquid state at constant rates. Glass transitions are observed in two, three and four dimensions as a hysteresis between the cooling and heating curves. This hysteresis appears in the energy and pressure diagrams, and the scanning-rate dependence of the area and height of the hysteresis can be described by power laws. The one dimensional system does not experience a glass transition but its specific heat curve resembles the shape of the $D\geq 2$ results in the supercooled liquid regime above the glass transition. As $D$ increases, the radial distribution functions reflect reduced geometric constraints. Nearest-neighbor distances become smaller with increasing $D$ due to interactions between nearest and next-nearest neighbors. Simulation data for the glasses are compared with crystal and melting data obtained with a Lennard-Jones system with only one type of particle and we find that with increasing $D$ crystallization becomes increasingly more difficult.

cond-mat.dis-nn↗
arXiv2009

Dynamic heterogeneities in critical coarsening: Exact results for correlation and response fluctuations in finite-sized spherical models

We study dynamic heterogeneities in the out-of-equilibrium coarsening dynamics of the spherical ferromagnet after a quench from infinite temperature to its critical point. A standard way of probing such heterogeneities is by monitoring the fluctuations of correlation and susceptibility, coarse-grained over mesoscopic regions. We discuss how to define fluctuating coarse-grained correlations (C) and susceptibilities (Chi) in models where no quenched disorder is present. Our focus for the spherical model is on coarse-graining over the whole volume of $N$ spins, which requires accounting for N^{-1/2} non-Gaussian fluctuations of the spin. The latter are treated as a perturbation about the leading order Gaussian statistics. We obtain exact results for these quantities, which enable us to characterise the joint distribution of C and Chi fluctuations. We find that this distribution is qualitatively different, even for equilibrium above criticality, from the spin-glass scenario where C and Chi fluctuations are linked in a manner akin to the fluctuation-dissipation relation between the average C and Chi. Our results show that coarsening at criticality is clearly heterogeneous for d>4 and suggest that, as in other glassy systems, there is a well-defined timescale on which fluctuations across thermal histories are largest. Surprisingly, however, neither this timescale nor the amplitude of the heterogeneities increase with the age of the system, as would be expected from the growing correlation length. For d<4, the strength of the fluctuations varies on a timescale proportional to the age of the system; the corresponding amplitude also grows with age, but does not scale with the correlation volume as might have been expected naively.

cond-mat.dis-nn↗