arXiv subjects

Youjin Deng

Publications and source records attributed to Youjin Deng.

At least 19 recordsLinked to original sources

arXiv2026

Finite-Temperature Phase Transition and Logarithmic Quasi-Long-Range Order in the Two-dimensional Long-range Heisenberg Model

We investigate the two-dimensional classical Heisenberg ($N=3$) model with long-range (LR) interactions decaying as $1/r^{2+σ}$, focusing on the marginal case $σ=2$. Large-scale Monte Carlo simulations up to linear size $L=8192$ reveal a finite-temperature phase transition, in striking contrast to the short-range case where the system is asymptotically free. An adiabatic renormalization-group analysis shows that the LR interaction provides a positive contribution to the stiffness flow and gives rise to a weak continuous transition through non-topological spin-wave fluctuations. We show that the low-temperature phase exhibits a novel logarithmic quasi-long-range order (log-QLRO), with correlations decaying as $C(r)\sim(\ln r)^{-η_\ell}$ and vanishing magnetization in the strict thermodynamic limit. High-precision data confirm this picture, including the predicted identity $2πκ_Rη_\ell=N-1$, with $κ_R$ the renormalized spin stiffness. The decay, with $η_\ell\propto T$, is slower than any power law, making the phase practically indistinguishable from true long-range order in realistic systems. Our results establish a novel log-QLRO phase and a continuous transition beyond the Ginzburg-Landau-Wilson paradigm in the two-dimensional Heisenberg model at $σ=2$.

cond-mat.stat-mech↗

arXiv2026

Fractal dimensions of paths on three-dimensional random-walk traces

We study four paths that join the starting site to the final position of a simple random walk of $N=L^2$ steps on the infinite cubic lattice. The paths are selected on the walk trace---the graph of visited sites and traversed bonds---by different rules: the undirected shortest path $S_1$, the directed shortest path $S_2$, the time-respecting shortest path $S_3$, and the depth $D_e$ of the final site in a depth-first-search tree. Monte Carlo simulations for $L$ up to 32768 give mean lengths scaling as $L^{d_O}$, with $d_{S_1}=1.48005(9)$, $d_{S_2}=1.49868(5)$, $d_{S_3}=1.51205(5)$, and $d_{D_e}=1.7099(7)$, so that $d_{S_1}<d_{S_2}<d_{S_3}<d_{\rm LE}<d_{D_e}$, where $d_{\rm LE}=1.62400(5)$ is the known loop-erased-random-walk exponent. Imposing traversal directions increases the shortest-path exponent, and imposing time order increases it further; these constraints therefore change the scaling exponent, not only the amplitude. For every path, the standard deviation scales with the same exponent as the mean, so it is scale-invariant, unlike the visited-site mass; the rescaled length distributions collapse onto a finite-width scaling function. No analytical theory currently predicts these exponents; our results provide precise numerical benchmarks for future studies of path geometry on random-walk traces.

cond-mat.stat-mech↗

arXiv2026

Tensor network Monte Carlo study of the J1-J2 Ising model on the square lattice

The frustrated square-lattice J1-J2 Ising model exhibits rich magnetic phases, yet its phase transitions remain difficult to characterize due to critical slowing down in conventional Monte Carlo and truncation errors inherent to tensor renormalization group methods. We develop a tensor-network Monte Carlo (TNMC) algorithm for this frustrated model, which supports both open and periodic boundary conditions. For periodic lattices, we use a sweeping block-update strategy that updates spin blocks while fixing surrounding spins. To boost efficiency, we couple our sampler with histogram reweighting, and test each technique standalone to validate these independent optimizations. We perform extensive finite-size scaling analyses at g=0.55 and g=1.0, extracting apparent critical temperatures and effective thermal exponents from Binder-cumulant data. Our method offers an efficient, nearly bias-free path for large-scale simulations of J1-J2-type frustrated magnets under periodic boundaries and generalizes readily to other frustrated spin lattices.

cond-mat.stat-mech↗

arXiv2026

Spin fluctuations and nearly isotropic quasiparticles in the doped three-dimensional Hubbard model

Away from half filling and above its Neel temperature, the three-dimensional Hubbard model is a paramagnetic metal with antiferromagnetic spin fluctuations, where controlled momentum-resolved results have been lacking. Using connected-determinant diagrammatic Monte Carlo, we compute the momentum-resolved self-energy for n = 0.4-0.95, T/t = 0.05-0.33 and U/t = 4-8, and the full-zone spin susceptibility at twelve of these points, focusing on U/t = 4. At U/t = 4 and toward half filling the spin fluctuations become strong: for n = 0.7-0.9 at T/t = 0.14 they enhance the susceptibility peak up to sevenfold and raise the momentum-dependent part of the scattering rate to four to five times its second-order value. They are driven by an effective spin interaction screened to about 2U/3 and nearly uniform over the zone. Yet the peak height is set by the slightly smaller value of this interaction at the peak wave vector, and near magnetic order this small difference changes the height by a large factor. Two-particle self-consistent theory reproduces the peak because its sum rule fixes its single constant interaction near this value, but for n = 0.7-0.9 at T/t = 0.14 its self-energy overestimates the local scattering rate and underestimates the momentum-dependent part. Though strong, the fluctuations are short ranged, with a correlation length of at most about two lattice spacings, and for n = 0.7-0.9 and T/t >= 0.14 the scattering rate near the Fermi surface varies by at most about 1% at fixed band energy, without hot spots. At U/t = 4 dynamical mean-field theory (DMFT) reproduces the local scattering rate and quasiparticle weight within a few percent, and the nonlocal part it misses is approximately a function of the band energy. Strong spin fluctuations thus coexist with nearly isotropic quasiparticles, and the results provide a benchmark for extensions of DMFT and for spin-fluctuation theories.

cond-mat.str-el↗

arXiv2026

First-Principles Effective Mass in the Three-Dimensional Uniform Electron Gas

The quasiparticle effective mass $m^*$ of the three-dimensional uniform electron gas (UEG) is a fundamental Fermi-liquid parameter whose value and density dependence have remained controversial for decades. Using renormalized perturbation theory with explicit counterterms, we determine $m^*$ in the metallic regime ($r_s \le 6$) from first principles by two complementary routes -- the self-energy and the forward-scattering four-point vertex via the $p$-wave spin-symmetric Landau parameter $F_1^s$ -- that agree within uncertainties at each density through sixth renormalized order. The resulting $m^*/m$ remains close to unity throughout the metallic regime, with a shallow non-monotonic density dependence -- a minimum near $r_s\approx 1$ followed by a gentle upturn -- reflecting the interplay of exchange and dynamical screening in the self-energy, and disfavoring strong monotonic suppression. This finding supports a physical picture for the metallic UEG in which dominant charge correlations are concentrated in nearly forward scattering and generate only a weak $F_1^s$ component.

cond-mat.str-el↗

arXiv2026

Static spin exchange-correlation kernel of the uniform electron gas at finite temperature

We determine the temperature and momentum dependence of the static spin exchange--correlation kernel of the unpolarized three-dimensional uniform electron gas using variational diagrammatic Monte Carlo. The calculations cover metallic densities with Wigner--Seitz radii $r_s=1\!-\!4$ and temperatures $T/T_F=1/16\!-\!8$, where $T_F$ is the Fermi temperature. At low temperature, the calculated kernel approaches established ground-state parametrizations. Heating suppresses its Fermi-scale minimum and reduces its magnitude, while the relative momentum dependence evolves nonmonotonically through the warm-dense crossover. At the two highest temperatures studied, the spin kernel is nearly constant over $q \leq 2k_F$, where $k_F$ is the Fermi wave number. The charge kernel at $r_s=1$ retains pronounced momentum dependence under the same conditions, making a local approximation to the XC kernel more accurate in the spin channel over this interval. The directly sampled uniform response determines the XC free-energy curvature with respect to spin polarization, independently of a fitted polarization dependence. This curvature sets the interaction contribution to the free-energy cost of weak polarization and differs by several percent from the Groth--Dornheim--Bonitz parametrization at elevated temperatures. These results provide momentum-resolved reference data for finite-temperature spin-response theories and direct constraints on the spin dependence of thermal free-energy functionals.

cond-mat.str-el↗

arXiv2026

Recursive Improvement of a Differentiable Scientific Software Ecosystem

Differentiable programming connects scientific computation with gradient-based inference, learning and design. Extending these capabilities across a heterogeneous software ecosystem requires specialized effort to implement derivatives, integrate interfaces and evaluate quality. AI coding agents can accelerate this transformation, but translating their capabilities into useful scientific software requires identifying research needs and evaluating how well implementations meet them. We present an environment for agent-driven evolution of differentiable scientific software that connects demand identification, development and quality evaluation. A unified differentiation interface exposes reusable derivative rules alongside existing numerical routines, allowing research tasks to share these capabilities. Research requirements guide development, with implementations assessed through independent derivative checks, workflow tests and performance evaluation. Validated software, research programs and tests become shared resources for subsequent studies. We construct and validate automatic differentiation extensions across 20 packages spanning physical, chemical and biological modeling, with research workflows demonstrating reuse across tasks. Benchmarks demonstrate computational savings over finite differences in gradient evaluation and complete parameter estimation. Research-driven revisions make previously unsupported workflows differentiable, correct derivatives of scientific observables and eliminate redundant computation. Quantum-control and thermal-design studies revise objectives in response to physical evaluation, improving designs while reusing existing derivatives. This work provides a practical approach to expanding differentiable programming across established scientific software and organizing AI agents around the recursive improvement of a shared computational ecosystem.

cs.AI↗

arXiv2026

Thermal Signatures of the Slater-Mott Crossover in the Hubbard Model: From Double Occupancy to Antiferromagnetic Correlation Length

The interaction-driven crossover from a Slater insulator to a Mott insulator in the Néel-ordered ground state of the Hubbard model is a fundamental paradigm of strongly correlated electrons, yet its quantitative characterization has remained elusive. Here we establish a clear and experimentally accessible thermal criterion for this crossover via the sign change of the temperature derivative of double occupancy, $(\partial D/\partial T)_U$, near zero temperature. In the Slater regime, $(\partial D/\partial T)_U>0$ reflects the major role of charge fluctuations; in the Mott regime, the anomalous $(\partial D/\partial T)_U<0$, a manifestation of the Pomeranchuk effect, signals the dominance of low-energy spin superexchange physics. Using exact diagonalization and {\it numerically exact} quantum Monte Carlo simulations, we demonstrate that this criterion determines the crossover boundary at $U_{\rm cross}/t=4.0(2)$ for the half-filled two-dimensional Hubbard model. Furthermore, we obtain a consistent boundary independently from the maximum in the antiferromagnetic correlation length, which also arises from the superexchange physics. These two thermal signatures are theoretically unified through the local minimum of thermal entropy versus interaction $U$ at low temperatures. Our results offer a direct, measurable, and physically intuitive framework to identify the Slater-Mott crossover in optical lattice experiments.

cond-mat.str-el↗

arXiv2026

OpenProblemBench: Benchmarking AI on Open Problems in the Foundational Theoretical Sciences

The next frontier for artificial general intelligence is tackling unresolved scientific problems, calling for benchmarks that assess progress beyond established knowledge. We introduce OpenProblemBench, a benchmark of 82 unresolved problems drawn from the mathematics and theoretical physics literature. Each problem supplies the research context, assumptions, and prior progress needed to investigate the question. We select problems whose proposed solutions admit comparatively clear checks of their decisive mathematical or computational claims. Four evaluator models independently assess the correctness, completeness, and degree of progress of each submission without reference solutions. Across seven evaluated configurations, GPT-6-Astra achieves the highest mean judged solve rate of 14.0%, compared with 5.5-6.7% for the evaluated full-size open models and 2.4-3.7% for Flash models. Case comparisons connect stronger outcomes to changes in problem representation, general arguments that extend beyond finite evidence, and proofs of the steps needed to complete a solution. By grounding evaluation in questions arising from the research literature, OpenProblemBench provides a setting for investigating the capabilities and limitations of AI as a contributor to foundational theoretical science.

cs.AI↗

arXiv2026

Spiral states, first-order transitions and specific heat multipeak phenomenon in $J_1$-$J_2$-$J_3$ Ising model: A Wang-Landau algorithm study

The classical $J_1$-$J_2$-$J_3$ Ising model on the honeycomb lattice is important for understanding frustrated magnetic phenomena in materials such as FePS$_3$ and Ba$_2$CoTeO$_6$, where diverse phases (e.g., striped, zigzag, armchair) and magnetization plateaus have been experimentally observed. To explain the experimental results, previous mean-field studies have explored its thermal phase transitions, identifying armchair phases and striped phases, but their limitations call for more reliable numerical investigations. In this work, we systematically revisit the classical $J_1$--$J_2$--$J_3$ Ising model using the Wang--Landau algorithm; in strongly frustrated parameter regimes where the Wang--Landau sampling becomes difficult, we further employ parallel tempering and a two-replica cluster algorithm combined with population annealing. We find that the armchair (AC) phase, previously reported in mean-field and experimental studies, actually coexists with the spiral (SP) phase, with their combined degeneracy reaching 20-fold (4-fold for the AC states and 16-fold for the spiral states). The phase transitions and critical exponents are studied at different interaction values. We observe first-order phase transitions, continuous phase transitions, and even the multipeak phenomenon in frustrated systems. These results clarify the nature of phases and phase transitions in frustrated Ising systems and their exponents, and additionally provide inspiration for experimental efforts to search for the spiral state and the specific-heat multipeak phenomenon.

cond-mat.str-el↗

arXiv2026

Scaling of Long-Range Loop-Erased Random Walks

We study the scaling properties of long-range loop-erased random walks (LR-LERW), where the underlying random walker performs Lévy-flight-like jumps with a power-law step-length distribution $P(\mathbf{r})\sim |\mathbf{r}|^{-(d+σ)}$. Using extensive Monte Carlo simulations, we measure the scaling relation $N \sim R^{d_N}$ between the loop-erased step number $N$ and the spatial extent $R$, and determine the geometric exponent $d_N$ for various values of $σ$ in spatial dimensions $d = 1, 2,$ and $3$, as well as at the marginal point $σ= 2$ in $d=4$ and $5$. We observe a continuous crossover from long-range (LR) to short-range (SR) behavior as $σ$ increases. Below the upper critical dimension $d<d_c=4$, for $σ< d/2$, loop erasure is asymptotically irrelevant and $d_N=σ$, consistent with Lévy-flight scaling. For $d/2 < σ< 2$, loop erasure becomes relevant and $d_N$ varies continuously toward the SR-LERW value. At the marginal points with $σ=d/2$ or $σ=2$, clear logarithmic corrections are observed. At and above the upper critical dimension, $d \geq 4$, the scaling at $σ=2$ is found to be $N \sim R^2/\ln R$, consistent with that of the corresponding Lévy flight. Our results provide a systematic numerical determination of $d_N(σ)$ for the LR-LERW across dimensions, and are consistent with $σ_* = 2$ as the boundary between LR and SR critical behaviors recently established in a broad variety of statistical models.

cond-mat.stat-mech↗

arXiv2026

Logarithmic Quasi-Long-Range Order and Novel Continuous Phase Transition in the Two-Dimensional $XY$ Model with $1/r^4$ Interaction

We investigate the phase diagram and critical properties of the two-dimensional classical XY model with interactions decaying as $1/r^{2+σ}$. At the marginal case $σ=2$, we show that the low-temperature phase is characterized by logarithmic quasi-long-range order (log-QLRO), where spin correlations decay as a power of the logarithm of distance, $C(r)\sim(\ln r)^{-η_\ell}$ with $η_\ell\propto T$, and that the transition into this phase is a continuous transition beyond both the Ginzburg-Landau-Wilson paradigm and the Berezinskii-Kosterlitz-Thouless mechanism. Our analysis combines a near-exact Gaussian spin-wave theory, an adiabatic renormalization-group analysis, and large-scale Monte Carlo simulations. We find that the $1/r^4$ interaction logarithmically modifies the spin-wave stiffness kernel as $γ(k)\simeqκk^2\ln(1/k)$, which suppresses vortex proliferation and gives rise to a nonuniversal correlation-length exponent $ν\propto1/\sqrt{2πκ}$. Crucially, our simulations reveal that the short-range algebraic QLRO phase is unstable against a weak long-range perturbation for $σ\le2$. These results establish $σ=2$ as the crossover boundary between the long-range and short-range universality classes and provide a critical evaluation of recent theoretical proposals.

cond-mat.stat-mech↗

arXiv2026

Intersection Exponents of Simple Random Walks in Two and Three Dimensions

The probability that several independent random walks avoid one another decays algebraically with the number of steps $N\to\infty$ in two and three dimensions, $P_N\sim N^{-ξ/2}$, where the intersection exponent $ξ$ depends on the number of random walks. More generally, one may consider several groups of independent random walks, with intersections allowed within each group and forbidden between different groups. We first study intersection exponents in two dimensions, where our results agree with the known exact formulas and test the numerical approach. In three dimensions, where no general exact expression is known, we determine $ξ$ for a range of cases. For two groups containing $k$ and $m$ random walks, respectively, we obtain the exponents $ξ(k,m)$ for $k=1,2$ and $m=1,2,\ldots,7$. We further extend $m$ to a continuous parameter $λ$, allowing us to obtain numerical values for $ξ(k,λ)$ for $k=1,2,3$ and $0.25\leqλ\leq3$. Away from the smallest moment orders, these functions increase with $λ$ with decreasing slopes, as expected from the strict concavity of Brownian intersection exponents. We also investigate three-group configurations for several representative cases. The resulting integer and continuous exponents supply numerical values for analytical studies of non-intersecting random paths.

cond-mat.stat-mech↗

arXiv2026

Long-range self-avoiding walk in one dimension: a Monte Carlo study

We study the one-dimensional long-range self-avoiding walk in the grand-canonical ensemble where the statistical weight of a jump of length $r$ decays algebraically as $r^{-(d+σ)}$. Using large-scale Monte Carlo simulations with an efficient irreversible update scheme, we obtain high-precision estimates of the critical fugacity $z_c$, the universal Binder ratio $Q_N^c$, the correlation-length exponent $ν$, and the anomalous dimension $η$. For $σ>1$, the critical fugacity varies smoothly with $σ$, while the Binder ratio and the critical exponents remain consistent with the short-range universality class. For $σ\le 1$, by contrast, the results clearly depart from short-range behavior, identifying $σ=1$ as the boundary between long-range and short-range regimes. In the long-range Wilson-Fisher regime with $1/2 < σ\leq 1$, $η$ agrees with the long-range Gaussian-fixed-point prediction $η_{\mathrm{GFP}}=2-σ$, whereas $Q_N^c$ and $ν$ vary nontrivially with $σ$ and exhibit discontinuous jumps at $σ=1$. These findings are in good agreement with the recently proposed universality diagram in the $(d,σ)$ plane for long-range O$(n)$ models, with the self-avoiding walk corresponding to the $n\to0$ limit.

cond-mat.stat-mech↗

arXiv2026

Persistence of BKT phase transition in the 2D nonanalytic XY model

We study the two-dimensional XY model with the nonanalytic pair potential $2[(1-\cosδ)/2]^{p}$, whose small-angle law $\propto|δ|^{2p}$ carries a cusp for $p<1$ and a flat bottom for $p>1$, invalidating the harmonic spin-wave expansion. Two questions arise: the nature of the low-temperature ($T$) phase and of the phase transition. A naive energetic argument would predict genuine long-range order and an enhanced transition temperature for $p<1$, and no transition at all for $p>1$. Large-scale Monte Carlo simulations contradict both: for every $p>0$ the \dengrevxxi{low-$T$ phase} is quasi-long-range ordered, with anomalous dimension $η(T)\propto T^{1/p}$, and terminates at a Berezinskii--Kosterlitz--Thouless transition. Using a vortex-free noncompact lattice-field description and utilizing a duality transformation, we show that coarse-graining drives the height-difference distribution onto a single Gaussian fixed point, renormalizing the cusp and flatness into a finite harmonic stiffness that restores the spin-wave description and the BKT scenario for all $p>0$.

cond-mat.stat-mech↗

arXiv2026

Computation of thermal entropy for the doped Hubbard Model

We develop a highly efficient framework for computing the thermal entropy in the doped Fermi-Hubbard model within the grand-canonical ensemble. The framework comprises four calculation schemes that express the entropy as path integrals in the parameter space of temperature, interaction strength, and chemical potential. The integrands involve only fundamental observables, including the total energy, fermion density, and double occupancy, which are readily accessible in a wide range of theoretical and numerical methods. We further derive useful Maxwell relations connecting the entropy to other quantities and present practical formulas for directly evaluating the grand potential. As an application, we compute the entropy of the doped Hubbard model in two and three dimensions, using the numerically unbiased auxiliary-field quantum Monte Carlo method. The test results show excellent agreement across the different schemes and quantitatively verify the Maxwell relations, confirming the reliability of the framework. In two dimensions, we further benchmark our entropy results in physically relevant parameter regimes against diagrammatic Monte Carlo calculations and observe excellent quantitative consistency between the two approaches. By providing an efficient and broadly applicable route for entropy evaluation, our work facilitates the thermodynamic characterization of complex correlated states in the doped Hubbard model.

cond-mat.str-el↗

arXiv2026

Emergent Equilibrium Structure Along a Critical Cluster Recursion

Critical universality does not determine the microscopic conditional structure of a probability measure. We study a bicolored cluster recursion constrained to remain critical at every generation, with no equilibrium spin measure or fixed coupling imposed. In both two and three dimensions, the resulting history-dependent sequence develops a common Ising/Fortuin--Kasteleyn (FK) compatibility structure: the second-shell dependence of a one-site conditional law is strongly suppressed, nearest-neighbor effective couplings move progressively toward one another near the critical Ising value, and cluster and interface observables organize around the corresponding FK geometry. An exact cluster-coloring factorization singles out $q=2$ as the point where the residual connectivity weight disappears from the two-color spin marginal. Thus equilibrium-compatible conditional structure can emerge along a trajectory that remains critical throughout.

cond-mat.stat-mech↗

arXiv2026

Exact autoregressive sampling of planar Ising spin glasses via the Kac--Ward theory

Exact sampling from the Boltzmann distribution of spin glasses remains an outstanding challenge: Markov chain Monte Carlo methods suffer from critical slowing down and metastable trapping, while modern neural autoregressive samplers such as variational autoregressive networks are approximate and, in the absence of exact reference samples, cannot be rigorously benchmarked. Here we present an exact autoregressive sampling algorithm for planar Ising spin glasses based on the Kac--Ward theory. Under the chain-rule factorization, sequentially fixing spins induces boundary-localized external fields, which destroy the zero-field structure required for exact evaluation. By encoding these fields with a planarity-preserving auxiliary spin construction, the conditional partition functions are mapped to an extended zero-field Ising model and exactly evaluated using the Kac--Ward determinant formula. The method generates strictly independent and identically distributed samples with exact normalized likelihoods at a computational cost of $\mathcal{O}(N^{5/2})$ for $N$ spins, thereby providing an exact baseline for benchmarking neural autoregressive samplers.

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