Weak Disorder Research Articles

On a Factorization Formula for the Partition Function of Directed Polymers

We prove a factorization formula for the point-to-point partition function associated with a model of directed polymers on the space-time lattice mathbb {Z}^{d+1}. The polymers are subject to a random potential induced by independent identically distributed random variables and we consider the regime of weak disorder, where polymers behave diffusively. We show that when writing the quotient of the point-to-point partition function and the transition probability for the underlying random walk as the product of two point-to-line partition functions plus an error term, then, for large time intervals [0, t], the error term is small uniformly over starting points x and endpoints y in the sub-ballistic regime Vert x - y Vert le t^{sigma }, where sigma < 1 can be arbitrarily close to 1. This extends a result of Sinai, who proved smallness of the error term in the diffusive regime Vert x - y Vert le t^{1/2}. We also derive asymptotics for spatial and temporal correlations of the field of limiting partition functions.

Public knowledge of early stroke symptoms in the Vilnius region

Background and aim. Stroke remains one of the most common causes of death and disability in the world. The evident decline in disabling outcomes can be attributed to the increasing use of reperfusion therapies. Stroke recognition and urgent admission of patients to specialized stroke centres after the onset of first stroke symptoms are essential for treatment outcomes. This study aims to assess public stroke awareness and its change since 2019.Methods. An anonymous cross-sectional study involving 300 Vilnius residents was conducted in 2022, the results of which were compared with the data of 502 respondents in 2019. A closed-ended questionnaire was used for the study. Statistical analysis was performed using IBM SPSS software with p&lt;0.05 significance level.Results. Stroke was identified as an acute cerebrovascular disorder by 83.3% of respondents in 2022 (82.7% in 2019). At least one correct warning sign of stroke was indicated by 98.7% of respondents (96.4% in 2019). The most commonly mentioned symptoms of stroke were one-sided face, arm or leg sensory disturbances, paralysis, or weakness (90.0%) and speech disorder (83.3%), with 82.1% and 81.5% respectively in 2019. Only 58% (45.4% in 2019) of respondents reported visual impairment as a stroke symptom. Women had better knowledge of stroke than men (p&lt;0.05). The internet was the main source of information for 63.3% of respondents (64.9% in 2019).Conclusions. Since 2019, stroke awareness has improved in Vilnius. This proves that F.A.S.T. campaign has reached the public. Women have better knowledge of stroke than men. Visual impairment is the least known symptom of stroke. Therefore, the search for new information programmes, especially directed to the targeted audience, can be useful for better publicity.

Quantum computation at the edge of a disordered Kitaev honeycomb lattice

We analyze propagation of quantum information along chiral Majorana edge states in two-dimensional topological materials. The use of edge states may facilitate the braiding operation, an important ingredient in topological quantum computations. For the edge of the Kitaev honeycomb model in a topological phase, we discuss how the edge states can participate in quantum-information processing, and consider a two-qubit logic gate between distant external qubits coupled to the edge. Here we analyze the influence of disorder and noise on properties of the edge states and quantum-gate fidelity. We find that realistically weak disorder does not prevent one from implementation of a high-fidelity operation via the edge.

Moments of Partition Functions of 2d Gaussian Polymers in the Weak Disorder Regime-I

Moments of Partition Functions of 2d Gaussian Polymers in the Weak Disorder Regime-I

Incomplete localization for disordered chiral strips

We prove that a disordered analog of the Su–Schrieffer–Heeger model exhibits dynamical localization (i.e., the fractional moment condition) at all energies except possibly zero energy, which is singled out by chiral symmetry. Localization occurs at arbitrarily weak disorder, provided it is sufficiently random. If furthermore the hopping probability measures are properly tuned so that the zero energy Lyapunov spectrum does not contain zero, then the system exhibits localization also at that energy, which is of relevance for topological insulators. The method also applies to the usual Anderson model on the strip.

Numerical evidence of a universal critical behavior of two-dimensional and three-dimensional random quantum clock and Potts models.

The random quantum q-state clock and Potts models are studied in two and three dimensions. The existence of Griffiths phases is tested in the two-dimensional case with q=6 by sampling the integrated probability distribution of local susceptibilities of the equivalent McCoy-Wu three-dimensional classical models with Monte Carlo simulations. For the random Potts model, numerical evidence of the existence of Griffiths phases is given and the finite-size effects are analyzed. For the clock model, the data also suggest the existence of a Griffiths phase but with much larger finite-size effects. The critical point of the random quantum clock model is then studied with the Strong-Disorder Renormalization Group. Evidence is given that, at strong enough disorder, this critical behavior is governed by the same infinite-disorder fixed point as the Potts model, for all the number of states q considered. At weak disorder, our renormalization group method becomes unstable and does not allow us to make conclusions.

Long range order for random field Ising and Potts models

AbstractWe present a new and simple proof for the classic results of Imbrie (1985) and Bricmont–Kupiainen (1988) that for the random field Ising model in dimension three and above there is long range order at low temperatures with presence of weak disorder. With the same method, we obtain a couple of new results: (1) we prove that long range order exists for the random field Potts model at low temperatures with presence of weak disorder in dimension three and above; (2) we obtain a lower bound on the correlation length for the random field Ising model at low temperatures in dimension two (which matches the upper bound in Ding–Wirth (2020)). Our proof is based on an extension of the Peierls argument with inputs from Chalker (1983), Fisher–Fröhlich–Spencer (1984), Ding–Wirth (2020) and Talagrand's majorizing measure theory (1980s) (and in particular, our proof does not involve the renormalization group theory).

Comorbid normochromic and normocytic anemia in coronary artery disease: retrospective study

The study's objective was to ascertain the prevalence and defining characteristics of anemia in coronary artery disease patients. Retrospectively, 534 patients with comorbid anemia and coronary artery disease were examined. All patients were determined to have ongoing coronary supply route infection. The normal time of examined patients was 76.2 ± 5.11. Males with hemoglobin levels below 13.5 mg/dL and females with hemoglobin levels below 11.5 mg/dL were diagnosed with comorbid anemia. The patients were randomized by sex, age, and type of coronary corridor infection. Among all analyzed patients with coronary vein sickness frailty is viewed as in almost 75% of cases, which matches with the writing information. In individuals after 50 pallor is more normal in men than in ladies, while in youthful and moderately aged patients weak condition is more run of the mill in females. Just in under 90 case reports the determination of frailty was kept in the last clinical analysis during patients' release from the emergency clinic, in one more case low hemoglobin level was not thought about by doctors. Roughly only 35% of all instances of serious paleness were not analyzed in a medical clinic and no fitting rectification of hemoglobin level was performed. The rate of sickliness doesn't rely upon the type of constant coronary vein infection. In many patients with coronary course sickness comorbid sickliness is of normochromic and normocytic character. Alongside movement of the seriousness of the comorbid paleness, a genuinely critical increment of the hospitalization time frame is noticed. In patients with coronary corridor sickness and comorbid pallor, the recurrence of hospitalizations each year is additionally expanded alongside iron deficiency level of seriousness. In conclusion, constant types of coronary corridor sickness in old and feeble patients in 69.89% of cases are confounded by comorbid paleness of various levels of seriousness. In more established patients with coronary course sickness, the weak disorder is most frequently brought about by respiratory illnesses, stomach ulcers, and duodenal ulcers, diseases of various limitations. In many patients with coronary conduit sickness comorbid sickliness is of normochromic and normocytic character.

Structural and spin-glass properties of single crystal J eff = ½ pyrochlore antiferromagnet NaCdCo2F7: correlating T f with magnetic-bond-disorder

Weak bond disorder disrupts the expected spin-liquid ground-state of the ideal S = 1/2 Heisenberg pyrochlore antiferromagnet. Here we introduce a single crystal study of the structural and magnetic properties of the bond-disordered pyrochlore NaCdCo2F7. The magnetic susceptibility appears isotropic, with a large negative Curie-Weiss temperature (θCW = −108(1) K), however no magnetic order is observed on cooling until a spin-glass transition at T f = 4.0 K. AC-susceptibility measurements show a frequency-dependent shift of the associated cusp in χ’ at T f, that can be fitted well by the empirical Vogel-Fulcher law. The magnetic moment of μ eff = 5.4(1) μ B/Co2+ indicates a significant orbital contribution and heat capacity measurements show that down to 1.8 K, well below T f, only S mag ∼ Rln(2) of the magnetic entropy is recovered, suggestive of residual continued dynamics. Structural and magnetism comparisons are made with the other known members of the NaA’’Co2F7 family (A″ = Ca2+, Sr2+), confirming the expected relationship between spin-glass freezing temperature, and extent of magnetic bond disorder brought about by the size mismatch between A-site ions.

Nutrition Assessment and Management of Late-Onset Tay-Sachs Disease: A Clinical Case Report.

Tay-Sachs disease is a sphingolipidoses disorder characterized by failure to produce enzymes necessary for the degradation of sphingolipids in lysosomes, which leads to muscle weakness, ataxia, and mental and speech disorders. The treatment for such disorders commonly includes the use of miglustat, a medication that may cause several side effects (e.g., diarrhea and weight loss) that can contribute to the development of malnutrition. To our knowledge, no reports are available in the literature on the nutritional assessment and intervention recommended for those with Tay-Sachs disease. This case report aimed to describe the case of a female patient diagnosed with late-onset Tay-Sachs disease. The patient presented with diarrhea (adverse effect to treatment) and malnutrition when referred to the dietitian. She had significant muscle loss, asthenia, and weakness. The nutritional interventions prescribed were: dietary modification; supplementation with beta-hydroxymethyl-butyrate (HMB); use of lactase enzyme; probiotic (Saccharomyces boulardii); and oral nutritional supplement with low osmolarity. Recommendations aimed to meet the patient's nutritional requirements, including energy needs. In response to the nutrition intervention, the patient progressed with diarrhea cessation, weight recovery, and improvement in physical function measured by the dynamometer. As patients undergoing treatment for Tay-Sachs disease quickly progress to malnutrition, and given the lack of guidelines to inform healthcare providers on nutritional recommendations for this cohort, the description of a case that had positive progression may inform healthcare providers and help to initiate a discussion on the need to conduct research in this field for the development of therapeutic protocols and nutrition recommendations.

Random magnetic field and the Dirac Fermi surface

We study a single two-dimensional Dirac fermion at finite density, subject to a quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1D chiral fermions (associated to each point on the Fermi surface) coupled by a random vector potential. This low-energy theory exhibits an exactly solvable random fixed line, along which we directly compute various disorder-averaged observables without the need for the usual replica, supersymmetry, or Keldysh techniques. We find the longitudinal dc conductivity in the collisionless $\ensuremath{\hbar}\ensuremath{\omega}/{k}_{B}T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit to be nonuniversal and to vary continuously along the fixed line.

Edge states in coupled non-Hermitian resonators.

Small perturbations may dramatically influence the physical properties of a single non-Hermitian cavity. However, how these small perturbations interplay with bulk-edge properties is still to be demonstrated by experimentation. Here, we experimentally demonstrate edge states in coupled non-Hermitian resonators, based on a chain of all-dielectric coupled resonators where each resonator consists of two target particles. The evanescent coupling between the cavity and the target particles leads to tunable asymmetric backscattering, which plays a key role in the appearance of edge states in the bulk bandgap. We also demonstrate that these observed edge states are robust against weak disorders introduced to the system. Our study may inspire further explorations of the non-Hermitian bulk-edge properties.

Enhancement of the magnetocaloric effect in geometrically frustrated cluster spin glass systems

In this work, we theoretically demonstrate that a strong enhancement of the magnetocaloric effect is achieved in geometrically frustrated cluster spin-glass systems just above the freezing temperature. We consider a network of clusters interacting randomly which have triangular structure composed of Ising spins interacting antiferromagnetically. The intercluster disorder problem is treated using a cluster spin glass mean-field theory, which allows exact solution of the disordered problem. The intracluster part can be solved using exact enumeration. The coupling between the inter and intracluster problem incorporates the interplay between effects coming from geometric frustration and disorder. As a result, it is shown that there is the onset of cluster spin glass phase even with very weak disorder. Remarkably, it is exactly within a range of very weak disorder and small magnetic field that is observed the strongest isothermal release of entropy.

Flat band induced metal-insulator transitions for weak magnetic flux and spin-orbit disorder

We consider manifolds of tunable all-bands-flat (ABF) lattices in dimensions $d=1,2$, parameterized by a manifold angle parameter $\ensuremath{\theta}$. We study localization properties of eigenstates in the presence of weak magnetic flux disorder and weak spin-orbit disorder. We demonstrate that weakly disordered ABF lattices are described by effective scale-free models, where the disorder strength is scaled out. For weak magnetic flux disorder, we observe subexponential localization at flatband energies in $d=1$, which differs from the usual Anderson localization. We also find diverging localization length at flatband energies for weak flux values in $d=2$; however, the character of the eigenstates at these energies is less clear. For weak spin-orbit coupling disorder in $d=2$ we identify a tunable metal-insulator transition with mobility edges. We also consider the case of mixed spin-orbit and diagonal disorder and obtain the metal-insulator transition driven by the manifold parameter $\ensuremath{\theta}$.

A stochastic reaction–diffusion modeling investigation of FLASH ultra-high dose rate response in different tissues

Purpose: The aim of the study was to propose a theory based on topology and geometry of diffusion channels in tissue to contribute to the mechanistic understanding of normal tissue sparing at ultra-high dose rates (UHDRs) and explore an interplay between intra- and inter-track radical recombination through a reaction–diffusion mechanism.Methods: We calculate the time evolution of particle track structures using a system of coupled reaction–diffusion equations on a random network designed for molecular transport in porous and disordered media. The network is representative of the intra- and inter-cellular diffusion channels in tissues. Spatial cellular heterogeneities over the scale of track spacing are constructed by incorporating random fluctuations in the connectivity between network sites, resembling molecular mass and charge heterogeneities at the cellular level.Results: We demonstrate the occurrence of phase separation among the tracks as the complexity in intra- and inter-cellular structure increases. At the strong limit of structural disorder, tracks evolve individually like isolated islands with negligible inter-track as they propagate like localized waves in space, analogous to the Anderson localization in quantum mechanics. In contrast, at the limit of weak disorder in a homogeneous medium, such as water, the neighboring tracks melt into each other and form a percolated network of non-reactive species. Thus, the spatiotemporal correlation among chemically active domains vanishes as the inter-cellular complexity of the tissue increases from normal tissue structure to fractal-type malignancy.Conclusion: Differential FLASH normal tissue sparing may result from the interplay of the proximity of tracks over the intra- and inter-cellular landscape, a transition in the spatial distribution of chemical reactivity, and molecular crowding. In this context, insensitivities in the radiobiological responses of the tumors to FLASH-UHDR are interpreted via a lack of geometrical correlation among isolated tracks. The structural and geometrical complexities of cancerous cells prevent the clustering of tracks over a timescale, in which inter-track chemical reactivities presumably prevail in normal tissues. A series of systematic experiments on radiolysis-induced diffusivity and reactivity in actual normal and cancerous tissues must be performed to classify the tissues potentially spared by FLASH-UHDRs and verify our theory.

Ab initio description of magnetic and critical properties of spin-glass pyrochlore NaSrMn2F7

In this study, I have investigated the magnetic and critical properties of manganese pyrochlore fluoride NaSrMn2F7, which exhibits a glass transition at Tf = 2.5 (K) due to charge disorder. A DFT + U + SOC framework is used in this paper to derive spin-Hamiltonian terms, including isotropic and anisotropic exchange interactions. An optimized geometry reveals a local distortion of the F–Mn–F angle along the ⟨111⟩ direction (95.48° and 84.51°), which is considered a weak bond disorder (δJ). Despite the complex structure of this material, first principle calculations show that its magnetic properties are only controlled by the nearest neighbor’s Heisenberg exchange interaction, and other interactions do not affect spin arrangements in the ground state. Thus, this material is considered a suitable candidate for studying electron correlation in spin glasses. Using a replica-exchange framework, Monte Carlo simulations indicate that with δJ=0, no phase transition is observed when magnetic susceptibility changes with temperature. The results demonstrate that the presence of local bond disorder serves as a perturbation, and the degeneracy of the energy manifold of the system persists if its effect is not taken into consideration. Based on δJ=0.13(meV) and the derived spin Hamiltonian, 2.6 (K) is obtained as the phase transition temperature.

Quantum transports in two-dimensions with long range hopping

We investigate the effects of disorder and shielding on quantum transports in a two dimensional system with all-to-all long range hopping. In the weak disorder, cooperative shielding manifests itself as perfect conducting channels identical to those of the short range model, as if the long range hopping does not exist. With increasing disorder, the average and fluctuation of conductance are larger than those in the short range model, since the shielding is effectively broken and therefore long range hopping starts to take effect. Over several orders of disorder strength (until sim 10^4 times of nearest hopping), although the wavefunctions are not fully extended, they are also robustly prevented from being completely localized into a single site. Each wavefunction has several localization centers around the whole sample, thus leading to a fractal dimension remarkably smaller than 2 and also remarkably larger than 0, exhibiting a hybrid feature of localization and delocalization. The size scaling shows that for sufficiently large size and disorder strength, the conductance tends to saturate to a fixed value with the scaling function beta sim 0, which is also a marginal phase between the typical metal (beta >0) and insulating phase (beta <0). The all-to-all coupling expels one isolated but extended state far out of the band, whose transport is extremely robust against disorder due to absence of backscattering. The bond current picture of this isolated state shows a quantum version of short circuit through long hopping.

Topological properties in an Aubry–André–Harper model with p-wave superconducting pairing

Abstract We study the topological properties of the one-dimensional p-wave Aubry–André–Harper (AAH) model with periodic incommensurate potential and transition coupling. The calculation results show that due to co-influence of the incommensurate potential and modulation phase, three topological phases arise in different parameter regions: a topologically trivial phase, Su–Schrieffer–Heeger (SSH)-like topological phase, and Kitaev-like topological superconducting phase with Majorana zero modes. By evaluating the Andreev reflection conductance, we see that in the Kitaev-like phase, the quantized conductance plateau comes into being at the zero-bias limit, due to the occurrence of resonant Andreev reflection. In addition, when the disorder effect is incorporated, the SSH-like topology is modified sensitively and the degenerate topological states split, whereas the Kitaev-like topological phase is robust to weak disorder. Finally, we find that disorder can induce topological phase transition, i.e. from the topologically trivial phase to the topological phase. Based on these results, we believe that our findings have significance for studying the topological phase transition in a one-dimensional topological superconducting system. Also, it provides a feasible scheme for clarifying different topological phases.

Free energy subadditivity for symmetric random Hamiltonians

We consider a random Hamiltonian H:Σ→R defined on a compact space Σ that admits a transitive action by a compact group G. When the law of H is G-invariant, we show its expected free energy relative to the unique G-invariant probability measure on Σ, which obeys a subadditivity property in the law of H itself. The bound is often tight for weak disorder and relates free energies at different temperatures when H is a Gaussian process. Many examples are discussed, including branching random walks, several spin glasses, random constraint satisfaction problems, and the random field Ising model. We also provide a generalization to quantum Hamiltonians with applications to the quantum Sherrington–Kirkpatrick and Sachdev–Ye–Kitaev models.

Analysis of urgent inpatient neurologic consultations in a large tertiary hospital center: Follow-up on the effect of standardized training of residents.

Clinical neurology is difficult for young residents. To familiarize with neurological emergencies as soon as possible for young doctors, the urgent inpatient neurologic consultations were analyzed. A retrospective study was conducted on the urgent inpatient neurologic consultations in a large tertiary hospital for 4 consecutive years. A total of 1437 cases were included, and the annual consultation cases gradually decreased from 573 to 257, involving 29 clinical departments. The disorders of urgent inpatient neurologic consultations were divided into three categories: neurological disorders (77.8%), non-neurological disorders (10.4%), and undiagnosed disorders (11.8%), common causes in consultation were disturbance of consciousness (36.0%), convulsions/stiffness (13.6%), limb weakness (8%), and mental disorder (5.6%). Common neurological disorders included acute cerebrovascular disease (33.6%), epilepsy/status epilepticus (15.8%), and metabolic or infectious toxic encephalopathy (14.9%). Urgent inpatient neurologic consultations involve multidisciplinary critical diseases, mainly neurological diseases. The standardized training of residents may help to rapidly improve the comprehensive diagnosis and treatment ability of young residents and is suitable for use in hospitals at all levels.