“The paper identifies universal polar dual pairs of spherical codes C and D such that for a large class of potential functions h the minima of the discrete h-potential of C on the sphere occur at the points of D and vice versa.”

“The paper determines the splitting field and a set of 68 linearly independent generators for the Mordell--Weil lattice of the elliptic surface.”

“The paper highlights that the heavy mass of Te atoms, weak Sn-Te bonding, and flat acoustic branches are key factors contributing to the ultralow lattice thermal conductivity.”

“The consistent value for the Hagedorn temperature, $T_{ m H} \simeq 0.34\, ext{GeV}$, for both mesons and baryons.”

“The regularized local markers eliminate the obstructive boundary irregularities successfully, and give rise to the desired global topological invariants such as the Chern number consistently when integrated over all the lattice sites.”

“The discovery of a direct second-order transition between the massless and symmetric massive fermion phases.”

“The droplet-to-slab transition always follows a similar mechanism to its equilibrium counterpart, but the reverse (slab-to-droplet) transition depends on rare non-equilibrium fluctuations.”

“The resulting thermodynamic pressure increases with temperature but exhibits an approximately logarithmic dependence.”

“Three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances.”

“The authors obtain accurate ground-state energies for lattices up to 80 x 80 (6400 spins) and train deep Boltzmann machines for a system with 35 x 35 (1225 spins).”

“The construction makes it possible to design infinite families of graphs on which exact and stable completion is possible for every fixed rank matrix through the sum-of-squares hierarchy.”

“The paper constructs a four-dimensional lattice-gas model with finite-range interactions that has non-periodic, ``quasicrystalline'' Gibbs states at low temperatures.”

“The oscillations are instead *enhanced*, decaying much slower than in the PXP limit.”

“Cube particles form a simple square assembly, overcoming lattice/topology incompatibility, and maximize entropy by distributing eight three-fold defects evenly on the sphere.”

“The paper finds that the mean of the first-passage probability may display a minimum as a function of bias strength, depending on the location of the initial and target sites relative to the focal point.”

“The paper demonstrates device-relevant ultrabroadband near-infrared (NIR) photonics by integrating element-specific roles within an entropy-stabilized lattice.”

“The study finds that the gluon helicity contribution to proton spin is $ΔG = 0.231(17)^{\mathrm{sta.}}(33)^{\mathrm{sym.}}$ at the $\overline{\mathrm{MS}}$ scale $μ^2=10\ \mathrm{GeV}^2$, which constitutes approximately $46(7)\%$ of the proton spin.”

“The paper proves that a cutoff phenomenon holds independently of the transition probabilities, subject only to the sub-Gaussian assumption and a minimal aperiodicity hypothesis.”

“Reconstruction is governed by a unified thermodynamic mechanism where high-index facets correspond to specific local minima in the surface energy landscape.”

“The paper introduces and analyzes a class of discrete Gaussian free fields on Hamming graphs, where interactions are determined solely by the Hamming distance between vertices.”

“The paper demonstrates the stabilization of 70 nm-radius skyrmions at room temperature and reveals how the Co and Gd sublattices influence the temperature-dependent net magnetization.”

“The paper finds a g-wave altermagnetic spin liquid as the unique ground state for the spin-3/2 model and a richer phase diagram for the spin-7/2 model, including d-wave altermagnetic spin liquids and chiral spin liquids.”

“The article's subject is the Yaglom theorem applied to critical branching random walk on Z^d.”

“The conductivity exhibits heavy-tailed fluctuations characterized by a power-law decay with exponent $α\approx 2.3$--$2.5$, indicating a finite mean but a divergent variance.”

“The article likely discusses the potential benefits of quantum machine learning in this specific context, such as improved computational efficiency or accuracy compared to classical methods.”

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“The paper finds a robust 4Q bipartite lattice of hedgehogs and antihedgehogs which melts through a first order phase transition.”

“The paper reveals a tunable regime of ergodicity breaking due to quantum many-body scars, manifested as long-lived coherent oscillations that persist across a much broader range of parameters than previously observed, including at the equilibrium phase transition point.”

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“The authors observe that the charge diffusion constant is well described by a simple functional dependence ~ 1/V^2 universally valid both for small and large V.”

“The article is sourced from ArXiv, indicating it's a pre-print or research paper.”

“The paper provides clear numerical evidences for anyon excitations with fractional charge and pronounced real-space density modulations, directly supporting the recently proposed anyon density-wave halo picture.”

“The analysis of all the data suggests that the anomalous CSL is not continuously connected to the high-frequency CSL.”

“The article is sourced from ArXiv, indicating it's a pre-print or research paper.”

“The paper introduces a new class of integrable 3D lattice models, possessing continuous families of commuting layer-to-layer transfer matrices.”

“The quantum Fisher information scales as $ \mathcal{F}_Q \sim L^{2p}$ (with L the lattice size and p the order of band touching) and $\mathcal{F}_Q \sim N^2 L^{2p}$ (with N the number of particles).”

“The mechanism enables controlled, sequential transitions between male and female states.”

“The paper highlights the scaling hypothesis for loop-length distributions, the emergence of critical exponents $τ=15/7$, $d_f=7/4$, and $σ=3/7$ in several universality classes.”

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“The paper introduces 'graph-restricted tensors' and demonstrates their utility in constructing non-stabilizer tensors for holographic models.”

“The resulting potential achieves density functional theory-level accuracy in reproducing a wide range of lattice defects in alpha-Fe and their interactions with hydrogen... it accurately captures the deformation and fracture behavior of nanopolycrystals containing hydrogen-segregated general grain boundaries.”

“The paper demonstrates the impressive performance of both quasi-continuum models in approximating the behavior of DDSWs and RWs.”

“Ce$^{3+}$ substitution at Sm$^{3+}$ sites transform the weak ferromagnetic (FM) $Γ_4$ state into robust AFM $Γ_1$ configuration through a gradual crossover.”

“The resulting evolution exhibits new features absent in the fully wetted case, including the coexistence of moving and pinned facets or the emergence and long-lived metastable states.”

“Both quantum models produced samples with lower average minimum distances to the true distribution compared to the LSTM, with the QCBM achieving the most favorable metrics.”

“The study likely contributes to the understanding of wave propagation in complex media.”

“The research likely investigates the potential for quantum computation using ultracold atoms.”

“The results revealed a consistent $λ_E(A)$ relationship, largely independent of lattice geometry (except for the smallest $A$).”

“The research investigates the potential of Hf/Zr superlattices and dipole layer engineering to enhance the performance of gate dielectrics in advanced CMOS.”

“The paper's core contribution is a "general and explicit construction recipe for QECCs from a total of D classical codes for arbitrary D." This allows for a broader exploration of QECC design space.”