Two-point Function Research Articles (Page 1)

Abstract Establishing microstructure–property correlations that generalize across diverse microstructural classes remains a critical challenge in data-driven materials design. In this work, we evaluate the potential to extrapolate predictive models trained on one microstructure type (e.g., spinodal) to others (e.g., dendritic), using three distinct featurization strategies: two-point correlation functions, graph-based descriptors, and deep neural network embeddings. Our findings reveal that the Wasserstein distance is an excellent metric that correlates well with generalizability, serving as a model-agnostic yet data-aware signature of generalizability. Furthermore, we demonstrate that featurizations that conserve key microstructural features generalize better. Graphic abstract

Abstract Understanding the large-scale structure of the Universe requires analyses of cosmic clustering and its evolution over time. In this work, we investigate the clustering properties of Sloan Digital Sky Survey blue galaxies, which are excellent tracers of dark matter, along two distinct epochs of the Universe, utilizing estimators like the two-point angular correlation function (2PACF), the angular power spectra, among others. Considering a model-independent approach, we perform analyses in two disjoint redshift shells, 0 ≤ z < 0.06 and 0.06 ≤ z < 0.12, to investigate the distribution of large cosmic structures. Using Bayesian inference methods, we constrain the parameter that quantifies the galaxy clustering in the 2PACF, enabling us to perform comparisons among different regions on the sky and between different epochs in the Universe regarding the gravitational action on matter structures. Our analyses complement previous efforts to map large-scale structures in the Local Universe. In addition, this study reveals differences regarding the clustering of large cosmic structures, comparing two epochs of the Universe, and analyses done with diverse estimators. Results reveal, clearly, distinct evolutionary signatures between the two redshift shells. Moreover, we had the opportunity to test the concordance cosmological model under extreme conditions in the highly nonlinear Local Universe, computing the amplitude of the angular power spectrum at very small scales. Ultimately, all our analyses serve as a set of consistency tests of the concordance cosmological model, the ΛCDM.

Abstract We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom associated to a Galerkin discretization as the fundamental lattice variables. We formulate standard concepts in lattice field theory, such as the partition function and correlation functions, in terms of the degrees of freedom. For example, using continuous finite element spaces, we show that the two-point spatial correlation function can be defined between any two points on the domain (as opposed to at just lattice sites) and furthermore, this two-point satisfies a weak propagator (or Green's function) identity, in analogy to the continuum case, as well as a convergence estimate obtained from the standard finite element techniques. Furthermore, this framework leads naturally to higher-order formulations of lattice field theories by considering higher-order finite element spaces for the Galerkin discretization. We consider analytical and numerical examples of scalar field theory to investigate how increasing the order of piecewise polynomial finite element spaces affect the approximation of lattice observables. Finally, we sketch an outline of this Galerkin framework in the context of gauge field theories.

We present an efficient method for extracting energy levels from lattice QCD correlation functions by computing the eigenvalues of the transfer matrix associated with the lattice QCD Hamiltonian. While mathematically and numerically equivalent to the recently introduced Lanczos procedure [1], our approach introduces a novel prescription for removing spurious eigenvalues using a kernel density estimator and Gaussian-convoluted histogram method. This strategy yields a robust and stable estimate of the energy spectrum, outperforming the Cullum-Willoughby filtering technique in efficiency. In addition, we detail how this method can be applied to extract overlap factors from two-point correlation functions, as well as matrix elements from three-point functions with a current insertion. Furthermore, we extend the methodology to accommodate correlation matrices constructed from a variational basis of operators, with its block formulation. We demonstrate the efficacy of this framework by computing the two lowest energy levels for a broad range of hadrons, including several nuclei. Although the signal-to-noise ratio is not significantly improved, the extracted energy levels are found to be more reliable than those obtained with conventional techniques. Within a given statistical ensemble, the proposed method effectively captures both statistical uncertainties and systematic errors, including those arising from the choice of fitting window, making it a robust and practical tool for lattice QCD analysis.

Abstract We consider the three-dimensional rotating motions of neutron stars blown by the “axion wind”. Neutron star precession and spin can change from the magnetic moment coupling to the oscillating axion background field, in analogy to the gyroscope motions with a driving force and the laboratory Nuclear Magnetic Resonance(NMR) detections of the axion. This effect modulates the pulse arrival time of the pulsar timing arrays. It shows up as a signal on the timing residual and two-point correlation function on the recent data of Nanograv and PPTA. The current measurement of PTAs can thus cast constraints on the axion-nucleon coupling as $g_\text{ann} \sim 10^{-12}\text{GeV}^{-1}$

Abstract We measure the projected two-point correlation functions of emission-line galaxies (ELGs) from the Dark Energy Spectroscopic Instrument One-Percent Survey and model their dependence on stellar mass and [O II] luminosity. We select ∼180,000 ELGs with redshifts of 0.8 < z < 1.6, and define 27 samples according to cuts in redshift and both galaxy properties. Following a framework that describes the conditional [O II] luminosity–stellar mass distribution as a function of halo mass, we simultaneously model the clustering measurements of all samples at fixed redshift. Based on the modeling result, most ELGs in our samples are classified as central galaxies, residing in halos of a narrow mass range with a typical median of ∼1012.2−12.4 h −1 M ⊙. We observe a weak dependence of clustering amplitude on stellar mass, which is reflected in the model constraints and is likely a consequence of the 0.5 dex measurement uncertainty in the stellar mass estimates. The model shows a trend between galaxy bias and [O II] luminosity at high redshift (1.2 < z < 1.6) that is otherwise absent at lower redshifts.

Abstract This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions $$d>4$$ d > 4 . Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. A companion paper proposes a similar analysis for spread-out Bernoulli percolation in dimensions $$d>6$$ d > 6 [10].

Abstract This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions $$d>6$$ d > 6 . We obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. In a companion paper, we apply a similar analysis to the study of the weakly self-avoiding walk model in dimensions $$d>4$$ d > 4 [Duminil-Copin and Panis, arXiv:2410.03649, (2024)].

Abstract A non-uniqueness phase for infinite clusters is proven for a class of marked random connection models (RCMs) on the d-dimensional hyperbolic space, ${\mathbb{H}^d}$ , in a high volume-scaling regime. The approach taken in this paper utilizes the spherical transform on ${\mathbb{H}^d}$ to diagonalize convolution by the adjacency function and the two-point function and bound their $L^2\to L^2$ operator norms. Under some circumstances, this spherical transform approach also provides bounds on the triangle diagram that allows for a derivation of certain mean-field critical exponents. In particular, the results are applied to some Boolean and weight-dependent hyperbolic RCMs. While most of the paper is concerned with the high volume-scaling regime, the existence of the non-uniqueness phase is also proven without this scaling for some RCMs whose resulting graphs are almost surely not locally finite.

Abstract We consider a four-dimensional globally hyperbolic and asymptotically flat spacetime (M, g) conformal to Minkowski spacetime, together with a massless, conformally coupled scalar field. Using a bulk-to-boundary correspondence, one can establish the existence of an injective $$*$$ ∗ -homomorphism $$\Upsilon _M$$ Υ M between $$\mathcal {W}(M)$$ W ( M ) , the Weyl algebra of observables on M and a counterpart which is defined intrinsically on future null infinity $$\Im ^+\simeq \mathbb {R}\times \mathbb {S}^2$$ ℑ + ≃ R × S 2 , a component of the conformal boundary of (M, g). Using invariance under the asymptotic symmetry group of $$\Im ^+$$ ℑ + , we can individuate thereon a distinguished two-point correlation function whose pull-back to M via $$\Upsilon _M$$ Υ M identifies a quasi-free Hadamard state for the bulk algebra of observables. In this setting, if we consider $$\textsf{V}^+_x$$ V x + , a future light cone stemming from $$x\in M$$ x ∈ M as well as $$\mathcal {W}(\textsf{V}^+_x)=\mathcal {W}(M)|_{\textsf{V}^+_x}$$ W ( V x + ) = W ( M ) | V x + , its counterpart at the boundary is the Weyl subalgebra generated by suitable functions localized in $$\textsf{K}_x$$ K x , a positive half strip on $$\Im ^+$$ ℑ + . To each such cone, we associate a standard subspace of the boundary one-particle Hilbert space, which coincides with the one associated naturally to $$\textsf{K}_x$$ K x . We extend such correspondence replacing $$\textsf{K}_x$$ K x and $$\textsf{V}^+_x$$ V x + with deformed counterparts, denoted by $$\textsf{S}_C$$ S C and $$\textsf{V}_C$$ V C . In addition, since the one particle Hilbert space at the boundary decomposes as a direct integral on the sphere of U(1)-currents defined on the real line, we prove that also the generator of the modular group associated to the standard subspace of $$\textsf{V}_C$$ V C decomposes as a suitable direct integral. This result allows us to study the relative entropy between coherent states of the algebras associated to the deformed cones $$\textsf{V}_C$$ V C establishing the quantum null energy condition.

We explore the evolving relationship between galaxies and their dark matter halos from z ∼ 0.1 to z ∼ 12 using mass-limited angular clustering measurements in the 0.54 deg2 of the COSMOS-Web survey, the largest contiguous JWST extragalactic survey. This study provides the first measurements of the mass-limited two-point correlation function at z ≥ 10 and a consistent analysis spanning 13.4 Gyr of cosmic history, setting new benchmarks for future simulations and models. Using a halo occupation distribution (HOD) framework, we derived characteristic halo masses and the stellar-to-halo mass ratio (SHMR) across redshifts and stellar mass bins. Our results first indicate that HOD models fit data at z ≥ 2.5 best when incorporating a nonlinear scale-dependent halo bias, boosting clustering at nonlinear scales (r = 10 − 100 kpc). We find that galaxies at z ≥ 10.5 with log(M⋆/M⊙)≥8.85 are predominantly central galaxies in halos with Mh ∼ 1010.5 M⊙, achieving a star formation efficiency (SFE) of εSF = M⋆/(fbMh) up to 1 dex higher than at z ≤ 1. The high galaxy bias at z ≥ 8 suggests that these galaxies reside in massive halos with an intrinsic high SFE, challenging stochastic SHMR scenarios. Our SHMR evolves significantly with redshift, starting very high at z ≥ 10.5, decreasing until z ∼ 2 − 3, then increasing again until the present. Current hydrodynamical simulations fail to reproduce both massive high-z galaxies and this evolution, while semi-empirical models linking SFE to halo mass, accretion rates, and redshift align with our findings. We propose that early galaxies (z > 8) experience bursty star formation without significant feedback altering their growth, driving the rapid growth of massive galaxies observed by JWST. Over time, the increasing feedback efficiency and the exponential halo growth end up suppressing star formation. At z ∼ 2 − 3 and later, the halo growth slows down, while star formation continues, supported by gas reservoirs in halos.

Abstract We investigate the clustering of Lyman-break galaxies at redshifts of 3 ≲ z ≲ 5 within the COSMOS field by measuring the angular two-point correlation function. Our robust sample of ~60,000 bright (mUV ≲ 27) Lyman-break galaxies was selected based on spectral energy distribution fitting across 14 photometric bands spanning optical and near-infrared wavelengths. We constrained both the 1- and 2-halo terms at separations up to 300 arcsec, finding an excess in the correlation function at scales corresponding to <20 kpc, consistent with enhancement due to clumps in the same galaxy or interactions on this scale. We then performed Bayesian model fits on the correlation functions to infer the Halo Occupation Distribution parameters, star formation duty cycle, and galaxy bias in three redshift bins. We examined several cases where different combinations of parameters were varied, showing that our data can constrain the slope of the satellite occupation function, which previous studies have fixed. For an MUV-limited sub-sample, we found galaxy bias values of $b_g=3.18^{+0.14}_{-0.14}$ at z ≃ 3, $b_g=3.58^{+0.27}_{-0.29}$ at z ≃ 4, $b_g=4.27^{+0.25}_{-0.26}$ at z ≃ 5. The duty cycle values are $0.62^{+0.25}_{-0.26}$, $0.40^{+0.34}_{-0.22}$, and $0.39^{+0.31}_{-0.20}$,respectively. These results suggest that, as the redshift increases, there is a slight decrease in the host halo masses and a shorter timescale for star formation in bright galaxies, at a fixed rest-frame UV luminosity threshold.

We consider a theory of fermions interacting with a (in general, non-Abelian) gauge field. The theory is assumed to be essentially inhomogeneous, which might be provided by nontrivial background fields interacting with both fermions and gauge bosons. For this theory, a version of Wigner-Weyl calculus is developed, in which the Wigner transformation of the fermion Green function belongs to a matrix representation of the gauge group. We demonstrate the power of the proposed formalism through the representation of responses of vector and axial currents to the gauge field strength through the topological invariants composed of the Wigner transformed two-point Green functions. This way, a new family of nondissipative transport phenomena is introduced. In particular, we discuss the non-Abelian versions of the chiral separation effect and of the quantum Hall effect.

We investigate the impact of disorder in the form of impurity scattering on a generalized version of the circular photogalvanic effect (CPGE) in Weyl semimetals where the frequency detuning between the two orthogonally polarized beams is nonzero. Considering a minimal model with two Weyl nodes at different energies, we employ the self-consistent Born approximation to unravel the dependence of the associated two-point retarded Green's function on the strength of intra- and internode scattering, frequency detuning, and energy difference between the two Weyl nodes. In the case of intranode scattering only, the second-order current density acquires Drude-like features, which we elucidate further by introducing an effective scattering strength. The Drude-like theory can even describe the second-order response in the presence of strong internode scattering, provided the latter has a linear interdependence with the intranode scattering. By properly adjusting the frequency detuning, we also find the real part of the two-point retarded Green's function to be reminiscent of a “quantized CPGE”-like form, although the imaginary part of the latter function is in general finite, and the second-order current density oscillates with time due to the finite frequency detuning. We finally conclude with an outlook on possible experimental consequences.

ABSTRACT The k-nearest neighbour (NN) cumulative distribution functions (CDFs) are measures of clustering for discrete data sets that are fast and efficient to compute. They are significantly more informative than the two-point correlation function. Their connection to N-point correlation functions, void probability functions, and counts-in-cells is known. However, the connections between the CDFs and geometric and topological summary statistics are yet to be fully explored. This understanding will be crucial to find optimally informative summary statistics to analyse data from stage-4 cosmological surveys. We explore quantitatively the geometric interpretations of the kNN CDF summary statistics. We establish an equivalence between the 1NN CDF at radius r and the volume of spheres with the same radius around data points. We show that higher kNN CDFs represent the volumes of intersections of $\ge k$ spheres around data points. We present similar geometric interpretations for the kNN cross-correlation CDFs. We further show that the full shape of the CDFs have information about planar angles, solid angles, and arc lengths created at the intersections of spheres around the data points, and can be accessed through the derivatives of the CDF. We show that this information is equivalent to that captured by Germ–Grain Minkowski Functionals. Using Fisher analyses, we compare the constraining power of various data vectors constructed from kNN CDFs and Minkowski Functionals. We find that the CDFs and their derivatives and the Minkowski Functionals have nearly identical constraining power. However, the CDFs are computationally orders of magnitude faster to evaluate.

Abstract We present here the first lattice simulation of symplectic quantization, a new functional approach to quantum field theory which allows to define an algorithm to numerically sample the quantum fluctuations of fields directly in Minkowski space-time, at variance with all other present approaches. Symplectic quantization is characterized by a Hamiltonian deterministic dynamics evolving with respect to an additional time parameter τ analogous to the fictious time of Parisi-Wu stochastic quantization. The difference between stochastic quantization and the present approach is that the former is well defined only for Euclidean field theories, while the latter allows to sample the causal structure of space-time. In this work we present the numerical study of a real scalar field theory on a 1+1 space-time lattice with a λϕ 4 interaction. We find that for λ ≪ 1 the two-point correlation function obtained numerically reproduces qualitatively well the shape of the free Feynman propagator. Within symplectic quantization the expectation values over quantum fluctuations are computed as dynamical averages along the dynamics in τ, in force of a natural ergodic hypothesis connecting Hamiltonian dynamics with a generalized microcanonical ensemble. Analytically, we prove that this microcanonical ensemble, in the continuum limit, is equivalent to a canonical-like one where the probability density of field configurations is P [ϕ] ∝ exp(zS[ϕ]/ℏ). The results from our simulations correspond to the value z = 1 of the parameter in the canonical weight, which in this case is a well-defined probability density for field configurations in causal space-time, provided that a lower bounded interaction potential is considered. The form proposed for P [ϕ] suggests that our theory can be connected to ordinary quantum field theory by analytic continuation in the complex-z plane.

Abstract Two-dimensional conformal field theories (CFTs) defined on non-orientable Riemann surfaces obey consistency Cardy conditions analogous to those in the orientable case. We revisit those conditions for irrational theories with central charge c > 1 in the context of two-point functions of primaries on the Real Projective plane $$ {\mathbbm{RP}}^2 $$ RP 2 and the partition function on the Klein bottle $$ {\mathbbm{K}}^2 $$ K 2 . Using the irrational versions of the Virasoro fusion and modular kernels we derive universal expressions for the non-orientable CFT data at large conformal dimension, assuming a gap in the spectrum of scalar primaries. In particular, we derive asymptotic formulas at finite central charge for the averaged Light-Light-Heavy product C LLH × Γ H of OPE coefficients with the $$ {\mathbbm{RP}}^2 $$ RP 2 one-point function normalizations, as well as for the parity-weighted density of heavy scalar primaries (or equivalently the density of heavy $$ {\Gamma}_H^2 $$ Γ H 2 ). We discuss the gravitational interpretation of the results.

ABSTRACT Surveys of cosmological large-scale structure (LSS) are sensitive to the presence of local primordial non-Gaussianity (PNG), and may be used to constrain models of inflation. Local PNG, characterized by $f_{\mathrm{NL}}$, the amplitude of the quadratic correction to the potential of a Gaussian random field, is traditionally measured from LSS two-point and three-point clustering via the power spectrum and bi-spectrum. We propose a framework to measure $f_{\mathrm{NL}}$ using the configuration space two-point correlation function (2pcf) monopole and three-point correlation function (3pcf) monopole of survey tracers. Our model estimates the effect of the scale-dependent bias induced by the presence of PNG on the 2pcf and 3pcf from the clustering of simulated dark matter haloes. We describe how this effect may be scaled to an arbitrary tracer of the cosmological matter density. The 2pcf and 3pcf of this tracer are measured to constrain the value of $f_{\mathrm{NL}}$. In LSS surveys, the effect of imaging systematics on two-point statistics is often degenerate with the PNG signal. Our proposed model employs three-point statistics primarily to break this degeneracy. Using simulations of luminous red galaxies observed by the Dark Energy Spectroscopic Instrument (DESI), we demonstrate the accuracy and constraining power of our method. Our forecast indicates the ability to constrain $f_{\mathrm{NL}}$ to a precision of $\sigma _{f_{\mathrm{NL}}} \approx 22$ with one year of DESI survey data, as well as the ability to constrain the imaging systematic weights in situ.

Abstract Thermal two-point functions in holographic CFTs receive contributions from two parts. One part comes from the identity, the stress tensor and multi-stress tensors and constitutes the stress-tensor sector. The other part consists of contributions from double-trace operators. The sum of these two parts must satisfy the KMS condition — it has to be periodic in Euclidean time. The stress-tensor sector can be computed by analyzing the bulk equations of motions near the AdS boundary and is not periodic by itself. We show that starting from the expression for the stress-tensor sector one can impose the KMS condition to fix the double-trace part, and hence the whole correlator. We perform explicit calculations in the asymptotic approximation, where the stress-tensor sector can be computed exactly. One can either sum over the thermal images of the stress-tensor sector and subtract the singularities or solve for the KMS condition directly and perform the Borel resummation of the resulting double-trace data — the results are the same.

Abstract We study SU(N) spin systems that mimic the behavior of particles in N-dimensional de Sitter space for N = 2, 3. Their Hamiltonians describe a dynamical system with hyperbolic fixed points, leading to emergent quasinormal modes at the quantum level. These manifest as quasiparticle peaks in the density of states. For a particle in 2-dimensional de Sitter, we find both principal and complementary series densities of states from a PT-symmetric version of the Lipkin-Meshkov-Glick model, having two hyperbolic fixed points in the classical phase space. We then study different spectral and dynamical properties of this class of models, including level spacing statistics, two-point functions, squared commutators, spectral form factor, Krylov operator and state complexity. We find that, even though the early-time properties of these quantities are governed by the saddle points — thereby in some cases mimicking corresponding properties of chaotic systems, a close look at the late-time behavior reveals the integrable nature of the system.