arXiv subjects

Daniel S. Fisher

Publications and source records attributed to Daniel S. Fisher.

At least 19 recordsLinked to original sources

arXiv2026

Low-temperature transition of 2d random-bond Ising model and quantum infinite randomness

At low temperatures, the classical two-dimensional random bond Ising model undergoes a frustration-driven ferromagnet-to-paramagnet transition controlled by a zero-temperature fixed point separating ferromagnet and spin glass phases. We show that this critical point can be understood through a renormalization group transformation that constructs the ground state of the Ising model through a sequence of Hamiltonians that, starting with an unfrustrated model, iteratively adds in frustration until the target Hamiltonian is reached. Via a mapping of the thermodynamics of the 2d Ising model to the spectral properties of a related Hermitian matrix -- the Hamiltonian of a noninteracting quantum problem -- this RG procedure corresponds to an iterative diagonalization of the quantum Hamiltonian. The flow toward zero temperature in the Ising picture manifests as a flow toward infinite randomness in the spectrum of the quantum Hamiltonian, with the log gap of the Hamiltonian scaling as a power of the system size: $\log \varepsilon_{\it min}^{-1} \sim L^ψ$. The tunneling exponent $ψ$ is equal to the spin stiffness exponent $θ_c$ characterizing the zero-temperature fixed point.

cond-mat.stat-mech↗

arXiv2024

Continual Evolution in Nonreciprocal Ecological Models

Feedbacks between evolution and ecology are ubiquitous, with ecological interactions determining which mutants are successful, and these mutants in turn modifying community structure. We study the evolutionary dynamics of several ecological models with overlapping niches, including consumer resource and Lotka-Volterra models. Evolution is assumed slow and extinctions are permanent, with ecological dynamics reaching a stable fixed point between introductions of invaders or mutants. When new strains are slowly added to the community, the ecosystem converges, after an initial evolutionary transient, to a diverse eco-evolutionary steady state. In this "Red Queen" phase of continual evolution, the biodiversity continues to turn over without the invasion probability of new variants getting any smaller. For resource-mediated interactions, the Red Queen phase obtains for any amount of asymmetry in the interactions between strains, and is robust to "general fitness" differences in the intrinsic growth rates of strains. Via a dynamical mean field theory framework valid for high-dimensional phenotype space, we analytically characterize the Red Queen eco-evolutionary steady state in a particular limit of model parameters. Scaling arguments enable a more general understanding of the steady state and evolutionary transients toward it. This work therefore establishes simple models of continual evolution in an ecological context without host-pathogen arms races, and points to the generality of Red Queen evolution. However, we also find other eco-evolutionary phases in simple models: For generalized Lotka-Volterra models with weakly asymmetric interactions an "oligarch" phase emerges in which the evolutionary dynamics continually slow down and a substantial fraction of the community's abundance condenses into a handful of slowly turning-over strains.

q-bio.PE↗

arXiv2014

The acceleration of evolutionary spread by long-range dispersal

The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also on the dispersal behavior of the species. Spreading at a constant speed is generally predicted when dispersal is sufficiently short-ranged. However, the case of long-range dispersal is unresolved: While it is clear that even rare long-range jumps can lead to a drastic speedup, it has been difficult to quantify the ensuing stochastic growth process. Yet such knowledge is indispensable to reveal general laws for the spread of modern human epidemics, which is greatly accelerated by aviation. We present a simple iterative scaling approximation supported by simulations and rigorous bounds that accurately predicts evolutionary spread for broad distributions of long distance dispersal. In contrast to the exponential laws predicted by deterministic "mean-field" approximations, we show that the asymptotic growth is either according to a power-law or a stretched exponential, depending on the tails of the dispersal kernel. More importantly, we provide a full time-dependent description of the convergence to the asymptotic behavior which can be anomalously slow and is needed even for long times. Our results also apply to spreading dynamics on networks with a spectrum of long-range links under certain conditions on the probabilities of long distance travel and are thus relevant for the spread of epidemics.

q-bio.PE↗

arXiv2012

Asexual Evolution Waves: Fluctuations and Universality

In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is still not fully understood, fundamentally because the effects of fluctuations due to the small numbers of the fittest individuals are large even in enormous populations. In this paper, branching processes and various asymptotic methods for analyzing the stochastic dynamics are further developed and used to obtain information on fluctuations, time dependence, and the distributions of sizes of subpopulations, jumps in the mean fitness, and other properties. The focus is on the behavior of a broad class of models: those with a distribution of selective advantages of available beneficial mutations that falls off more rapidly than exponentially. For such distributions, many aspects of the dynamics are universal - quantitatively so for extremely large populations. On the most important time scale that controls coalescent properties and fluctuations of the speed, the dynamics is reduced to a simple stochastic model that couples the peak and the high-fitness "nose" of the fitness distribution. Extensions to other models and distributions of available mutations are discussed briefly.

q-bio.PE↗

arXiv2012

Genetic Diversity and the Structure of Genealogies in Rapidly Adapting Populations

Positive selection distorts the structure of genealogies and hence alters patterns of genetic variation within a population. Most analyses of these distortions focus on the signatures of hitchhiking due to hard or soft selective sweeps at a single genetic locus. However, in linked regions of rapidly adapting genomes, multiple beneficial mutations at different loci can segregate simultaneously within the population, an effect known as clonal interference. This leads to a subtle interplay between hitchhiking and interference effects, which leads to a unique signature of rapid adaptation on genetic variation both at the selected sites and at linked neutral loci. Here, we introduce an effective coalescent theory (a "fitness-class coalescent") that describes how positive selection at many perfectly linked sites alters the structure of genealogies. We use this theory to calculate several simple statistics describing genetic variation within a rapidly adapting population, and to implement efficient backwards-time coalescent simulations which can be used to predict how clonal interference alters the expected patterns of molecular evolution.

q-bio.PE↗

arXiv2011

Rate of Adaptation in Large Sexual Populations

Adaptation often involves the acquisition of a large number of genomic changes which arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later. In large populations, when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously. We calculate the rate of adaptation, v, in several models of such sexual populations and show that v is linear in NU_b only in sufficiently small populations. In large populations, v increases much more slowly as log NU_b. The prefactor of this logarithm, however, increases as the square of the recombination rate. This acceleration of adaptation by recombination implies a strong evolutionary advantage of sex.

q-bio.PE↗

arXiv2006

On the universality of jamming percolation: reply to the comment of Jeng and Schwarz

In Phys. Rev. Lett. 96, 035702 (2006) we introduced a class of kinetically constrained models which display a dynamical glass transition. We focused on a particular example: the "knights" model. As correctly pointed out by Jeng and Schwarz cond-mat/0612484, we overlooked some additional directed frozen structures of the knights model which are not simple directed percolation (DP) paths: these "thicker" directed structures lower the critical density. Here we argue that, nevertheless, the full directed processes are in the DP universality class and the T-junctions between perpendicular segments of these give rise to a jamming percolation transition with the universal properties discussed in our previous work. Moreover, we present other models for which all our previous results, included the value of the critical density, hold rigorously.

cond-mat.stat-mech↗

arXiv2006

Beneficial mutation-selection balance and the effect of linkage on positive selection

When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population concurrently. In an asexual population, these different mutant lineages interfere and not all can fix simultaneously. In addition, further beneficial mutations can accumulate in mutant lineages while these are still a minority of the population. In this paper, we analyze the dynamics of such multiple mutations and the interplay between multiple mutations and interference between clones. These result in substantial variation in fitness accumulating within a single asexual population. The amount of variation is determined by a balance between selection, which destroys variation, and beneficial mutations, which create more. The behavior depends in a subtle way on the population parameters: the population size, the beneficial mutation rate, and the distribution of the fitness increments of the potential beneficial mutations. The mutation-selection balance leads to a continually evolving population with a steady-state fitness variation. This variation increases logarithmically with both population size and mutation rate and sets the rate at which the population accumulates beneficial mutations, which thus also grows only logarithmically with population size and mutation rate. These results imply that mutator phenotypes are less effective in larger asexual populations. They also have consequences for the advantages (or disadvantages) of sex via the Fisher-Muller effect; these are discussed briefly.

q-bio.PE↗

arXiv2005

Jamming Percolation and Glass Transitions in Lattice Models

A new class of lattice gas models with trivial interactions but constrained dynamics are introduced. These are proven to exhibit a dynamical glass transition: above a critical density, rho_c, ergodicity is broken due to the appearance of an infinite spanning cluster of jammed particles. The fraction of jammed particles is discontinuous at the transition, while in the unjammed phase dynamical correlation lengths and timescales diverge as exp[C(rho_c-rho)^(-mu)]. Dynamic correlations display two-step relaxation similar to glass-formers and jamming systems.

cond-mat.stat-mech↗

arXiv2005

Superconductor-to-Metal Transitions in Dissipative Chains of Mesoscopic Grains and Nanowires

The interplay of quantum fluctuations and dissipation in chains of mesoscopic superconducting grains is analyzed, and the results are also applied to nanowires. It is shown that in 1-d arrays of resistively shunted Josephson junctions, the superconducting-normal charge relaxation within the grains plays an important role. At zero temperature, two superconducting phases can exist, depending primarily on the strength of the dissipation. In the fully superconducting phase (FSC), each grain acts superconducting, and the coupling to the dissipative conduction is important. In the SC* phase, the dissipation is irrelevant at long wavelengths. The phase transitions between these two superconducting phases and the normal metallic phase may be either local or global, and possess rich and complex critical properties. These are inferred from both weak and strong coupling renormalization group analyses. At intermediate temperatures, near either superconductor-to-normal phase transition, there are regimes of super-metallic behavior, in which the resistivity first decreases gradually with decreasing temperature before eventually increasing as temperature is lowered further. The results on chains of Josephson junctions are extended to continuous superconducting nanowires and the subtle issue of whether these can exhibit an FSC phase is considered. Potential relevance to superconductor-metal transitions in other systems is also discussed.

cond-mat.supr-con↗

arXiv2005

Scenario for Spin Glass Phase with Infinitely Many States

A possible phase in short-range spin glasses exhibiting infinitely many equilibrium states is proposed and characterized in real space. Experimental signatures in equilibrating systems measured with scanning probes are discussed. Some models with correlations in their exchange interactions are argued to exhibit this phase. Questions are raised about more realistic models and related issues.

cond-mat.dis-nn↗

arXiv2004

Spatial structures and dynamics of kinetically constrained models for glasses

Kob and Andersen's simple lattice models for the dynamics of structural glasses are analyzed. Although the particles have only hard core interactions, the imposed constraint that they cannot move if surrounded by too many others causes slow dynamics. On Bethe lattices a dynamical transition to a partially frozen phase occurs. In finite dimensions there exist rare mobile elements that destroy the transition. At low vacancy density, $v$, the spacing, $Ξ$, between mobile elements diverges exponentially or faster in $1/v$. Within the mobile elements, the dynamics is intrinsically cooperative and the characteristic time scale diverges faster than any power of $1/v$ (although slower than $Ξ$). The tagged-particle diffusion coefficient vanishes roughly as $Ξ^{-d}$.

cond-mat.dis-nn↗

arXiv2003

Energy Correlations In Random Transverse Field Ising Spin Chains

The end-to-end energy - energy correlations of random transverse-field quantum Ising spin chains are computed using a generalization of an asymptotically exact real-space renormalization group introduced previously. Away from the critical point, the average energy - energy correlations decay exponentially with a correlation length that is the same as that of the spin - spin correlations. The typical correlations, however, decay exponentially with a characteristic length proportional to the square root of the primary correlation length. At the quantum critical point, the average correlations decay sub-exponentially as $\bar{C_{L}}\sim e^{-const\cdot L^{1/3}}$, whereas the typical correlations decay faster, as $\sim e^{-K\sqrt{L}}$, with $K$ a random variable with a universal distribution. The critical energy-energy correlations behave very similarly to the smallest gap, computed previously; this is explained in terms of the RG flow and the excitation structure of the chain. In order to obtain the energy correlations, an extension of the previously used methods was needed; here this was carried out via RG transformations that involve a sequence of unitary transformations.

cond-mat.dis-nn↗

arXiv2003

Dissipation and quantum phase transitions of a pair of Josephson junctions

A model system consisting of a mesoscopic superconducting grain coupled by Josephson junctions to two macroscopic superconducting electrodes is studied. We focus on the effects of ohmic dissipation caused by resistive shunts and superconducting-normal charge relaxation within the grain. As the temperature is lowered, the behavior crosses over from uncoupled Josephson junctions, similar to situations analyzed previously, to strongly interacting junctions. The crossover temperature is related to the energy-level spacing of the grain and is of the order of the inverse escape time from the grain. In the limit of zero temperature, the two-junction system exhibits five distinct quantum phases, including a novel superconducting state with localized Cooper pairs on the grain but phase coherence between the leads due to Cooper pair cotunneling processes. In contrast to a single junction, the transition from the fully superconducting to fully normal phases is found to be controlled by an intermediate coupling fixed point whose critical exponents vary continuously as the resistances are changed. The model is analyzed via two component sine-Gordon models and related Coulomb gases that provide effective low temperature descriptions in both the weak and the strong Josephson coupling limits. The complicated phase diagram is consistent with symmetries of the two component sine-Gordon models, which include weak to strong coupling duality and permutation triality. Experimental consequences of the results and potential implications for superconductor to normal transitions in thin wires and films are discussed briefly.

cond-mat.supr-con↗

arXiv2002

Spin Reduction Transition in Spin-3/2 Random Heisenberg Chains

Random spin-3/2 antiferromagnetic Heisenberg chains are investigated using an asymptotically exact renormalization group. Randomness is found to induce a quantum phase transition between two random-singlet phases. In the strong randomness phase the effective spins at low energies are S_eff=3/2, while in the weak randomness phase the effective spins are S_eff=1/2. Separating them is a quantum critical point near which there is a non-trivial mixture of S=1/2, S=1, and S=3/2 effective spins at low temperatures.

cond-mat.dis-nn↗

arXiv2002

Quantum Collective Creep: a Quasiclassical Langevin Equation Approach

The dynamics of an elastic medium driven through a random medium by a small applied force is investigated in the low-temperature limit where quantum fluctuations dominate. The motion proceeds via tunneling of segments of the manifold through barriers whose size grows with decreasing driving force $f$. In the limit of small drive, at zero-temperature the average velocity has the form $v\propto\exp[-{\rm const.}/\hbar^α f^μ]$. For strongly dissipative dynamics, there is a wide range of forces where the dissipation dominates and the velocity--force characteristics takes the form $v\propto\exp[-S(f)/\hbar]$, with $S(f)\propto 1/ f^{(d+2ζ)/(2-ζ)}$ the action for a typical tunneling event, the force dependence being determined by the roughness exponent $ζ$ of the $d$-dimensional manifold. This result agrees with the one obtained via simple scaling considerations. Surprisingly, for asymptotically low forces or for the case when the massive dynamics is dominant, the resulting quantum creep law is {\it not} of the usual form with a rate proportional to $\exp[-S(f)/\hbar]$; rather we find $v\propto \exp\{-[S(f)/\hbar]^2\}$ corresponding to $α=2$ and $μ= 2(d+2ζ-1)/(2-ζ)$, with $μ/2$ the naive scaling exponent for massive dynamics. Our analysis is based on the quasi-classical Langevin approximation with a noise obeying the quantum fluctuation--dissipation theorem. The many space and time scales involved in the dynamics are treated via a functional renormalization group analysis related to that used previously to treat the classical dynamics of such systems. Various potential difficulties with these approaches to the multi-scale dynamics -- both classical and quantum -- are raised and questions about the validity of the results are discussed.

cond-mat.dis-nn↗

arXiv2002

Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior

A model of an elastic manifold driven through a random medium by an applied force F is studied focussing on the effects of inertia and elastic waves, in particular {\it stress overshoots} in which motion of one segment of the manifold causes a temporary stress on its neighboring segments in addition to the static stress. Such stress overshoots decrease the critical force for depinning and make the depinning transition hysteretic. We find that the steady state velocity of the moving phase is nevertheless history independent and the critical behavior as the force is decreased is in the same universality class as in the absence of stress overshoots: the dissipative limit which has been studied analytically. To reach this conclusion, finite-size scaling analyses of a variety of quantities have been supplemented by heuristic arguments. If the force is increased slowly from zero, the spectrum of avalanche sizes that occurs appears to be quite different from the dissipative limit. After stopping from the moving phase, the restarting involves both fractal and bubble-like nucleation. Hysteresis loops can be understood in terms of a depletion layer caused by the stress overshoots, but surprisingly, in the limit of very large samples the hysteresis loops vanish. We argue that, although there can be striking differences over a wide range of length scales, the universality class governing this pseudohysteresis is again that of the dissipative limit. Consequences of this picture for the statistics and dynamics of earthquakes on geological faults are briefly discussed.

cond-mat.dis-nn↗

arXiv2001

The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states

The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim L^ζ$, is consistent with the theoretical prediction $ζ= 2/3$. As the randomness is increased through the transition, the probability distribution of the interfacial tension of domain walls scales as for a single second order transition. At the critical point, the fractal dimensions of domain walls and the fractal dimension of the outer surface of spin clusters are investigated: there are at least two distinct physically important fractal dimensions. These dimensions are argued to be related to combinations of the energy scaling exponent, $θ$, which determines the violation of hyperscaling, the correlation length exponent $ν$, and the magnetization exponent $β$. The value $β= 0.017\pm 0.005$ is derived from the magnetization: this estimate is supported by the study of the spin cluster size distribution at criticality. The variation of configurations in the interior of a sample with boundary conditions is consistent with the hypothesis that there is a single transition separating the disordered phase with one ground state from the ordered phase with two ground states. The array of results are shown to be consistent with a scaling picture and a geometric description of the influence of boundary conditions on the spins. The details of the algorithm used and its implementation are also described.

cond-mat.dis-nn↗