arXiv subjects

Michael Hinczewski

Publications and source records attributed to Michael Hinczewski.

At least 55 records · Page 3Linked to original sources

arXiv2011

Phase Separation and Charge-Ordered Phases of the d = 3 Falicov-Kimball Model at T>0: Temperature-Density-Chemical Potential Global Phase Diagram from Renormalization-Group Theory

The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The CO phases occur at and near half filling of the conduction electrons for the entire range of localized electron densities. The phase boundaries are second order, except for the intermediate and large interaction regimes, where a first-order phase boundary occurs in the central region of the phase diagram, resulting in phase coexistence at and near half filling of both localized and conduction electrons. These two-phase or three-phase coexistence regions are between different charge-ordered phases, between charge-ordered and disordered phases, and between dense and dilute disordered phases. The second-order phase boundaries terminate on the first-order phase transitions via critical endpoints and double critical endpoints. The first-order phase boundary is delimited by critical points. The cross-sections of the global phase diagram with respect to the chemical potentials and densities of the localized and conduction electrons, at all representative interactions strengths, hopping strengths, and temperatures, are calculated and exhibit ten distinct topologies.

cond-mat.stat-mech↗

arXiv2011

Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension

We introduce an anisotropic mean-field approach for the dynamics of semiflexible polymers under intermediate tension, the force range where a chain is partially extended but not in the asymptotic regime of a nearly straight contour. The theory is designed to exactly reproduce the lowest order equilibrium averages of a stretched polymer, and treats the full complexity of the problem: the resulting dynamics include the coupled effects of long-range hydrodynamic interactions, backbone stiffness, and large-scale polymer contour fluctuations. Validated by Brownian hydrodynamics simulations and comparison to optical tweezer measurements on stretched DNA, the theory is highly accurate in the intermediate tension regime over a broad dynamical range, without the need for additional dynamic fitting parameters.

cond-mat.soft↗

arXiv2011

Deconvolution of dynamic mechanical networks

Time-resolved single-molecule biophysical experiments yield data that contain a wealth of dynamic information, in addition to the equilibrium distributions derived from histograms of the time series. In typical force spectroscopic setups the molecule is connected via linkers to a read-out device, forming a mechanically coupled dynamic network. Deconvolution of equilibrium distributions, filtering out the influence of the linkers, is a straightforward and common practice. We have developed an analogous dynamic deconvolution theory for the more challenging task of extracting kinetic properties of individual components in networks of arbitrary complexity and topology. Our method determines the intrinsic linear response functions of a given molecule in the network, describing the power spectrum of conformational fluctuations. The practicality of our approach is demonstrated for the particular case of a protein linked via DNA handles to two optically trapped beads at constant stretching force, which we mimic through Brownian dynamics simulations. Each well in the protein free energy landscape (corresponding to folded, unfolded, or possibly intermediate states) will have its own characteristic equilibrium fluctuations. The associated linear response function is rich in physical content, since it depends both on the shape of the well and its diffusivity---a measure of the internal friction arising from such processes like the transient breaking and reformation of bonds in the protein structure. Starting from the autocorrelation functions of the equilibrium bead fluctuations measured in this force clamp setup, we show how an experimentalist can accurately extract the state-dependent protein diffusivity using a straightforward two-step procedure.

q-bio.BM↗

arXiv2011

Tensor Renormalization Group: Local Magnetizations, Correlation Functions, and Phase Diagrams of Systems with Quenched Randomness

The tensor renormalization-group method, developed by Levin and Nave, brings systematic improvability to the position-space renormalization-group method and yields essentially exact results for phase diagrams and entire thermodynamic functions. The method, previously used on systems with no quenched randomness, is extended in this study to systems with quenched randomness. Local magnetizations and correlation functions as a function of spin separation are calculated as tensor products subject to renormalization-group transformation. Phase diagrams are extracted from the long-distance behavior of the correlation functions. The approach is illustrated with the quenched bond-diluted Ising model on the triangular lattice. An accurate phase diagram is obtained in temperature and bond-dilution probability, for the entire temperature range down to the percolation threshold at zero temperature.

cond-mat.stat-mech↗

arXiv2011

Compaction and tensile forces determine the accuracy of folding landscape parameters from single molecule pulling experiments

We establish a framework for assessing whether the transition state location of a biopolymer, which can be inferred from single molecule pulling experiments, corresponds to the ensemble of structures that have equal probability of reaching either the folded or unfolded states (Pfold = 0.5). Using results for the forced-unfolding of a RNA hairpin, an exactly soluble model and an analytic theory, we show that Pfold is solely determined by s, an experimentally measurable molecular tensegrity parameter, which is a ratio of the tensile force and a compaction force that stabilizes the folded state. Applications to folding landscapes of DNA hairpins and leucine zipper with two barriers provide a structural interpretation of single molecule experimental data. Our theory can be used to assess whether molecular extension is a good reaction coordinate using measured free energy profiles.

cond-mat.soft↗

arXiv2010

DNA-Protein Binding Rates: Bending Fluctuation and Hydrodynamic Coupling Effects

We investigate diffusion-limited reactions between a diffusing particle and a target site on a semiflexible polymer, a key factor determining the kinetics of DNA-protein binding and polymerization of cytoskeletal filaments. Our theory focuses on two competing effects: polymer shape fluctuations, which speed up association, and the hydrodynamic coupling between the diffusing particle and the chain, which slows down association. Polymer bending fluctuations are described using a mean field dynamical theory, while the hydrodynamic coupling between polymer and particle is incorporated through a simple heuristic approximation. Both of these we validate through comparison with Brownian dynamics simulations. Neither of the effects has been fully considered before in the biophysical context, and we show they are necessary to form accurate estimates of reaction processes. The association rate depends on the stiffness of the polymer and the particle size, exhibiting a maximum for intermediate persistence length and a minimum for intermediate particle radius. In the parameter range relevant to DNA-protein binding, the rate increase is up to 100% compared to the Smoluchowski result for simple center-of-mass motion. The quantitative predictions made by the theory can be tested experimentally.

cond-mat.soft↗

arXiv2010

How the diffusivity profile reduces the arbitrariness of protein folding free energies

The concept of a protein diffusing in its free energy folding landscape has been fruitful for both theory and experiment. Yet the choice of the reaction coordinate (RC) introduces an undesirable degree of arbitrariness into the problem. We analyze extensive simulation data of an alpha-helix in explicit water solvent as it stochastically folds and unfolds. The free energy profiles for different RCs exhibit significant variation, some having an activation barrier, others not. We show that this variation has little effect on the predicted folding kinetics if the diffusivity profiles are properly taken into account. This kinetic quasi-universality is rationalized by an RC rescaling, which, due to the reparameterization invariance of the Fokker-Planck equation, allows the combination of free energy and diffusivity effects into a single function, the rescaled free energy profile. This rescaled free energy indeed shows less variation among different RCs than the bare free energy and diffusivity profiles separately do, if we properly distinguish between RCs that contain knowledge of the native state and those that are purely geometric in nature. Our method for extracting diffusivity profiles is easily applied to experimental single molecule time series data and might help to reconcile conflicts that arise when comparing results from different experimental probes for the same protein.

physics.bio-ph↗

arXiv2010

Frustrated Further-Neighbor Antiferromagnetic and Electron-Hopping Interactions in the d=3 tJ Model: Finite-Temperature Global Phase Diagrams from Renormalization-Group Theory

The renormalization-group theory of the d=3 tJ model is extended to further-neighbor antiferromagnetic or electron-hopping interactions, including the ranges of frustration. The global phase diagram of each model is calculated for the entire ranges of temperatures, electron densities, and further/first-neighbor interaction strength ratios. In addition to the τ_{tJ} phase seen in earlier studies of the nearest-neighbor d=3 tJ model, the τ_{Hb} phase seen before in the d=3 Hubbard model appears both near and away from half-filling. These distinct τphases potentially correspond to different (BEC-like and BCS-like) superconducting phases.

cond-mat.supr-con↗

arXiv2009

Critical Percolation Phase and Thermal BKT Transition in a Scale-Free Network with Short-Range and Long-Range Random Bonds

Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory, in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic (Berezinskii-Kosterlitz-Thouless) geometric order, occurs in the phase diagram, in addition to the ordinary (compact) percolating phase and the non-percolating phase. It is found that no connection exists between, on the one hand, the onset of this geometric BKT behavior and, on the other hand, the onsets of the highly clustered small-world character of the network and of the thermal BKT transition of the Ising model on this network. Nevertheless, both geometric and thermal BKT behaviors have inverted characters, occurring where disorder is expected, namely at low bond probability and high temperature, respectively. This may be a general property of long-range networks.

cond-mat.dis-nn↗

arXiv2009

Global cross-over dynamics of single semiflexible polymers

We present a mean-field dynamical theory for single semiflexible polymers which can precisely capture, without fitting parameters, recent fluorescence correlation spectroscopy results on single monomer kinetics of DNA strands in solution. Our approach works globally, covering three decades of strand length and five decades of time: it includes the complex cross-overs occurring between stiffness-dominated and flexible bending modes, along with larger-scale rotational and center-of-mass motion. The accuracy of the theory stems in part from long-range hydrodynamic coupling between the monomers, which makes a mean-field description more realistic. Its validity extends even to short, stiff fragments, where we also test the theory through Brownian hydrodynamics simulations.

cond-mat.soft↗

arXiv2009

Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.

cond-mat.dis-nn↗

arXiv2009

End-monomer dynamics in semiflexible polymers

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) r^2(t) ~ t^(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling r^2(t) ~ t^(2/3) in the same time range. We find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, alpha(t) = d log r^2(t)/ d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, in particular the variation of alpha(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent alpha are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales.

cond-mat.soft↗

arXiv2009

Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass

The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice. Five different ordered phases, namely ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase diagram. The spin-glass phase is more extensive when randomness is introduced within the planes than when it is introduced in lines along one direction. Phase diagram cross-sections, with no Nishimori symmetry, with Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are studied. The boundary between the ferromagnetic and spin-glass phases can be either reentrant or forward, that is either receding from or penetrating into the spin-glass phase, as temperature is lowered. However, this boundary is always reentrant when the multicritical point terminating it is on the Nishimori symmetry line.

cond-mat.dis-nn↗

arXiv2008

Excitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation

The anisotropic XXZ spin-1/2 Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated thoughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Isinglike ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction s_i^x s_j^x + s_i^y s_j^y induces an antiferromagnetic correlation in the out-of-plane s_i^z component, at higher temperatures in the antiferromagnetic XXZ chain, dominantly at low temperatures in the ferromagnetic XXZ chain, and, in-between, at all temperatures in the XY chain. We find that the converse effect also occurs in the antiferromagnetic XXZ chain: an antiferromagnetic s_i^z s_j^z interaction induces a correlation in the s_i^xy component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or XY) anisotropy; (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.

cond-mat.stat-mech↗

arXiv2007

High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows

The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10^-5 along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D = 24, corresponding to 4624-dimensional renormalization-group flows.

cond-mat.stat-mech↗

arXiv2007

Griffiths singularities and algebraic order in the exact solution of an Ising model on a fractal modular network

We use an exact renormalization-group transformation to study the Ising model on a complex network composed of tightly-knit communities nested hierarchically with the fractal scaling recently discovered in a variety of real-world networks. Varying the ratio K/J of of inter- to intra-community coupling, we obtain an unusual phase diagram: at high temperatures or small K/J we have a disordered phase with a Griffiths singularity in the free energy, due to the presence of rare large clusters, which we analyze through the Yang-Lee zeros in the complex magnetic field plane. As the temperature is lowered, true long-range order is not seen, but there is a transition to algebraic order, where pair correlations have power-law decay with distance, reminiscent of the XY model. The transition is infinite-order at small K/J, and becomes second-order above a threshold value (K/J)_m. The existence of such slowly decaying correlations is unexpected in a fat-tailed scale-free network, where correlations longer than nearest-neighbor are typically suppressed.

cond-mat.dis-nn↗

arXiv2006

d=3 Anisotropic and d=2 tJ Models: Phase Diagrams, Thermodynamic Properties, and Chemical Potential Shift

The anisotropic d=3 tJ model is studied by renormalization-group theory, yielding the evolution of the system as interplane coupling is varied from the isotropic three-dimensional to quasi-two-dimensional regimes. Finite-temperature phase diagrams, chemical potential shifts, and in-plane and interplane kinetic energies and antiferromagnetic correlations are calculated for the entire range of electron densities. We find that the novel tau phase, seen in earlier studies of the isotropic d=3 tJ model, and potentially corresponding to the superconducting phase in high-T_c materials, persists even for strong anisotropy. While the tau phase appears at low temperatures at 30-35% hole doping away from =1, at smaller hole dopings we see a complex lamellar structure of antiferromagnetic and disordered regions, with a suppressed chemical potential shift, a possible marker of incommensurate ordering in the form of microscopic stripes. An investigation of the renormalization-group flows for the isotropic two-dimensional tJ model also shows a pre-signature of the tau phase, which appears with finite transition temperatures upon addition of the smallest interplane coupling.

cond-mat.str-el↗

arXiv2006

Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network

We have obtained exact results for the Ising model on a hierarchical lattice with a scale-free degree distribution, high clustering coefficient, and small-world behavior. By varying the probability p of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly-clustered, small-world system is studied. We obtain analytical expressions for the degree distribution P(k) and clustering coefficient C for all p, as well as the average path length l for p=0 and 1. The Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to 562,500 probability bins to represent the distribution. For p < 0.494, we find power-law critical behavior of the magnetization and susceptibility, with critical exponents continuously varying with p, and exponential decay of correlations away from T_c. For p >= 0.494, where the network exhibits small-world character, the critical behavior radically changes: We find a highly unusual phase transition, namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with non-zero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length. Approaching T_c from below, the magnetization and the susceptibility respectively exhibit the singularities of exp(-C/sqrt(T_c-T)) and exp(D/sqrt(T_c-T)), with C and D positive constants. With long-range bond strengths decaying with distance, we see a phase transition with power-law critical singularities for all p, an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.

cond-mat.dis-nn↗