arXiv subjects

Youjin Deng

Publications and source records attributed to Youjin Deng.

At least 37 records · Page 2Linked to original sources

arXiv2026

Perturbative Renormalization and Universality Diagram for Long-Range Quantum Criticality

Experimental progress in quantum simulators highlights the role of long-range (LR) interactions in reshaping quantum criticality and stabilizing exotic phases beyond the short-range (SR) paradigm. We study ferromagnetic long-range quantum $O(n)$ models with interactions decaying as $1/r^{d+σ}$ and develop a perturbative renormalization-group expansion around the LR--SR boundary by setting $d=3-ε$ and $σ=2-δ$. In this parametrization, the full interacting LR window $2d/3<σ<2$ becomes $0<δ<2ε/3$, and is therefore perturbatively controlled. A two-loop calculation yields explicit expressions, in terms of $ε$, $δ$, and $n$, for the correlation-length exponent $ν$ and for the frequency and momentum anomalous dimensions $η_ω$ and $η_k$. The resulting exponents reduce to long-range Gaussian scaling at $σ=2d/3$ and to SR quantum Wilson-Fisher scaling in the $σ\to 2$ limit, thereby identifying $σ_*=2$ as the LR--SR boundary within the controlled $3-ε$ expansion. Combining the RG results with scaling boundaries and classical LR analogies, we propose a $(d,σ)$ universality diagram for ferromagnetic long-range quantum $O(n)$ criticality and use it as an organizing framework for the phase diagram of long-range quantum spin chains.

cond-mat.stat-mech↗

arXiv2026

Two-Electron Correlations in the Metallic Electron Gas

We present high-precision \emph{ab initio} calculations of the four-point vertex function for the three-dimensional uniform electron gas using variational diagrammatic Monte Carlo. From these results, we extract Landau parameters that reveal a density-driven crossover from underscreening to overscreening, and obtain the full two-electron scattering amplitude on the Fermi surface with controlled accuracy. A residual analysis of the scattering amplitude against the charge-channel Kukkonen--Overhauser (KO$^+$) interaction shows that only a minimal s-wave correction in the antiparallel-spin channel is needed, defining the sKO$^+$ ansatz: KO$^+$ within the local-density approximation plus this short-range correction. Using both our direct VDMC amplitudes and the sKO$^+$ ansatz, we compute the electron-electron contribution to the thermal resistivity, obtaining quantitative agreement with experiments on simple metals (Al, Na, K, Rb). sKO$^+$ thus provides a controlled UEG-based effective interaction for simple-metal transport and future first-principles extensions.

cond-mat.str-el↗

arXiv2026

Large-deviation tails of critical order-parameter distributions

Large-deviation tails of critical probability distributions provide a sensitive probe of universality beyond standard finite-size scaling. We study these tails for critical percolation and Fortuin--Kasteleyn Ising models on two-dimensional lattices, three-dimensional lattices, and complete graphs. We consider two rescaled order parameters: the magnetization-like variable $x_m=|M|/\langle |M|\rangle$, including a signed cluster-mass analogue for percolation, and the largest-cluster variable $x_C=C_1/\langle C_1\rangle$. For $x_m$, we test the expected stretched-exponential large-deviation tail and show that the same form applies to the percolation analogue. For $x_C$, guided by the exact complete-graph result and scaling arguments, we propose universal scaling forms for both tails of the cumulative distribution and test them by extensive Monte Carlo simulations. In the complete-graph FK-Ising model, the left tail is governed by rare configurations with percolation-like scaling rather than by the typical Ising scaling. Our results show that the tails of order-parameter distributions reveal universal features of critical fluctuations that are not captured by averaged observables alone.

cond-mat.stat-mech↗

arXiv2026

Algorithmic overlaps as thermodynamic variables: from local to cluster Monte Carlo dynamics in critical phenomena

We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two successive Wolff clusters reflects critical behavior and can be used as an order parameter for the algorithm's dynamics. In the case of the Swendsen-Wang algorithm, similar behavior is demonstrated by the variance of the overlap of two consecutive lattice configurations, which behaves like an order parameter. Nothing similar is observed for the Metropolis algorithm, where the dynamics in the critical region are determined by the spin-flip frequency, which is equivalent to the acceptance rate. Thus, the critical behavior of the Wolff cluster overlap and of the variance of the configuration overlap in the Swendsen-Wang algorithm are naturally related to the critical behavior of geometric objects -- Fortuin-Kasteleyn clusters. Interestingly, in all cases the geometric quantity -- the configuration overlap or its variance -- reflects the thermodynamics of the phase transition.

cond-mat.stat-mech↗

arXiv2026

Quantum Monte Carlo study of the metal-insulator crossover in the square-lattice Hubbard model

The interaction-driven evolution from a Fermi liquid to a Mott insulator is a hallmark of strongly correlated fermion systems. In this work, we present a {\it numerically unbiased} study of such metal-to-insulator crossover in the half-filled square-lattice Hubbard model at finite temperatures, employing auxiliary-field quantum Monte Carlo method. By jointly analyzing thermodynamic and dynamical observables, we establish the crossover diagram of the model in the temperature-interaction ($T$-$U$) plane. With increasing $U$, our numerical results reveal an extended crossover regime, which we refer to as the {\it Bad Metal}, that separates the Fermi liquid and Mott insulator. During the crossover, we also examine the antiferromagnetic spin correlations and observe pronounced nodal-antinodal dichotomy in the momentum-resolved single-particle spectral functions. Furthermore, we investigate the temperature dependence of several commonly used observables in the model. As representative results, we achieve an accurate map of the thermal entropy across the crossover diagram, and identify the parameter regions in which the model exhibits the Pomeranchuk cooling, characterized by an adiabatic cooling with increasing $U$. Beyond offering a more refined understanding of the crossover phenomenon, our work also provides valuable benchmark and guideline for future optical lattice experiments on the square-lattice Hubbard model.

cond-mat.str-el↗

arXiv2026

Spontaneous Symmetry Breaking in Two-dimensional Long-range Heisenberg Model

Algebraically decaying interactions $\sim 1/r^{d+σ}$ can lead to nontrivial universality beyond short-range (SR) theories and spontaneous symmetry breaking in low-dimensional systems. We perform large-scale Monte Carlo simulations for the classical long-range (LR) Heisenberg model in two dimensions (2D) up to linear size $L=8192$. We show that the system enters a long-range-ordered phase through a single continuous phase transition for all $σ\leq 2$, including the marginal case $σ=2$. In contrast, for $σ> 2$ it recovers the SR asymptotically free behavior with no finite-temperature transition. This places the LR--SR crossover threshold at $σ_* = 2$. To characterize the ordered phase, we introduce an LR simple random walk with a fixed total length $\mathcal{L} \sim\mathcal{O}(L^d)$. This fixed-$\mathcal L$ walk reproduces the finite-size scaling of the Goldstone-mode fluctuations in the LR Heisenberg model in both two and three dimensions, including the logarithmic scaling at $σ= 2$. These results further motivate a general criterion for the existence of finite-temperature long-range order in LR systems with continuous symmetry in any spatial dimension.

cond-mat.stat-mech↗

arXiv2026

Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter

The phase of spins in the quasi-two-dimensional (q2D) XY model has emerged as a topic of significant interest across multiple subfields of physics. Conventional wisdom, rooted in the Mermin-Wagner theorem and supported by existing paradigms, asserts that true long-range (LR) order is prohibited in q2D systems with continuous symmetries and short-range (SR) interactions. In this Letter, we propose a strictly SR q2D XY model defined on a plane perpendicularly intersected by a group of parallel planes, where each plane consists of XY spins coupled via nearest-neighbor interactions. Through large-scale Monte Carlo simulations complemented by finite-size scaling analysis, we establish the complete phase diagram of the setup. A LR ordered phase emerges in the q2D model when the spins on the parallel planes develop a Berezinskii-Kosterlitz-Thouless critical phase. The LR ordered phase is anisotropic: true LR correlations develop exclusively along the direction of the intersection lines, while the perpendicular direction exhibits quasi-long-range order. Furthermore, the LR order exhibits Goldstone-mode physics. Our findings reveal a mechanism for stabilizing LR order in low-dimensional systems with continuous symmetries, thereby establishing a new platform for studying exotic superfluidity.

cond-mat.stat-mech↗

arXiv2026

Ising models on the hydrogen peroxide and other lattices

We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to be relatively large. Combining the Monte Carlo results for the hydrogen peroxide lattice with those for five other three-dimensional lattices, we obtain a set of data covering a wide range of the irrelevant temperature field. This is helpful in the determination of the parameters describing the corrections to scaling. As a consequence, new results are obtained for the universal parameters describing Ising criticality in three dimensions, with reduced error margins in comparison with earlier Monte Carlo analyses. The critical exponents describing the thermodynamic singularities are determined by the temperature renormalization exponent $y_t = 1.58693 (9)$ and the magnetic renormalization exponent $y_h = 2.48178 (5)$. The corrections to scaling are governed by the irrelevant exponent $y_1 = -0.821 (5)$.

cond-mat.stat-mech↗

arXiv2026

Universality of percolation at dynamic pseudocritical point

Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point. Focusing on two-dimensional percolation, we show that the size distribution of the largest cluster asymptotically approaches to a Gumbel form in the subcritical phase, a Gaussian form in the supercritical phase, and transitions within the critical finite-size scaling window. Numerical results indicate that, at consistently defined pseudocritical points, this distribution exhibits a universal form across various lattices and percolation models (bond or site), within error bars, yet differs from the distribution at the critical point. The critical polynomial, universally zero for two-dimensional percolation at the critical point, becomes nonzero at pseudocritical points. Nevertheless, numerical evidence suggests that the critical polynomial, along with other dimensionless quantities such as wrapping probabilities and Binder cumulants, assumes fixed values at the pseudocritical point that are independent of the percolation type (bond or site) but vary with lattice structures. These findings imply that while strict universality breaks down at the pseudocritical point, certain extreme-value statistics and dimensionless quantities exhibit quasi-universality, revealing a subtle connection between scaling behaviors at critical and pseudocritical points.

cond-mat.stat-mech↗

arXiv2026

Equivalent-neighbor $k$-core percolation in two dimensions

We perform large-scale numerical simulations to investigate the critical behavior of $k$-core percolation in two dimensions with an extended interaction range $r$. By systematically varying both the core index $k$ and the interaction range $r$, we construct a comprehensive phase diagram in the $(k,r)$ plane. In contrast to $k$-core percolation in infinite dimensions, no hybrid transition is observed in two dimensions: the phase diagram contains only a continuous transition regime and a strictly first-order regime, separated by a tricritical or critical-end point $(k_s,r_s)$. For $k k_s$ and finite $r>r_s$, the transition is discontinuous, with no hybrid features or critical singularities. In this first-order regime, the pseudocritical point approaches the critical point as $1/\ln L$, where $L$ is the linear system size, distinct from the $L^{-d}$ scaling typical of conventional thermodynamic first-order transitions in $d$ dimensions. This logarithmic finite-size drift is consistent with a nucleation-driven mechanism, in which rare voids trigger the collapse of the finite-range $k$-core. These results demonstrate that geometric constraints can fundamentally alter the nature of $k$-core percolation found in finite dimensions.

cond-mat.stat-mech↗

arXiv2026

Emergent critical phases of the Ashkin-Teller model on the Union-Jack Lattice

The Ashkin-Teller (AT) model is a classic spin model in statistical mechanics. For traditional homogeneous lattices like triangular and kagome lattices, even when frustration exists, the model only has one ferromagnetic-paramagnetic critical line in the $J>0$ and $K<0$ region. However, in this paper, for the Union Jack lattice, where the lattice coordination numbers are 4, 8, and 8 and which also contains a large number of small triangular units, using Metropolis Monte Carlo method, we find that, the critical line of the AT model splits into two Berezinskii-Kosterlitz-Thouless(BKT) boundaries, and a critical phase emerges in the intermediate region. This phenomenon is the combined result of frustration, lattice inhomogeneity and the two coupled spin degrees of freedom inherent to the AT model. In detail, the novel critical phase characterized by a power-law decay of magnetization with system size, where the correlation length ratio $ξ/L$ remains finite even in the thermodynamic limit. We also introduce the susceptibility $\widetildeχ = \text{d}\langle m \rangle /\text{d}J$ as a key probe, and through this probe, pseudo-critical points $J_c(L)$ are observed to scale proportionally to $(\ln L)^{-2}$, a behavior consistent with BKT criticality. Since superfluids, superconductors, and supersolids all possess quasi-long-range order and fall into the category of critical phases, our results could also inspire the exploration of such quantum phases.

cond-mat.stat-mech↗

arXiv2026

Box model of quantum annealing

A particle-in-a-box model of continuous space quantum annealing is proposed and studied numerically by solving the Schrödinger wave equation directly. Three types of energy landscapes with multiple local minima are considered, namely a sinusoidal wave modulated by a concave, a convex, or a flat envelope. Both static (energy spectrum) and dynamical (residual energy) behaviors are analyzed in detail, paying particular attention to the effects of landscape roughness and annealing depth. Simulation results show that the residual energy as a function of annealing speed is largely independent of these two factors. The prevalence of diabatic transitions during annealing is observed, and the discrepancy between our numerical results and the Landau-Zener formula is discussed. An interesting feature in the energy gap spectrum, which we call flat gaps, is examined. Based on it, we propose a mechanism to explain the trapping of wave function in local minima during diabatic transitions, widely observed in our data.

quant-ph↗

arXiv2026

Emergent Slow Thinking in LLMs as Inverse Tree Freezing

Reinforcement learning with verifiable rewards (RLVR) enables large language models to acquire slow, multi-step reasoning from sparse final-answer signals. We provide a statistical-physics picture of this emergence. We show that an autoregressive model's finite capacity forces it to compress its exponentially large prefix space into a Markov network of predictive states, on which slow thinking unfolds as a random walk -- the Concept Network (CoNet) picture. Within CoNet, RLVR dynamics are governed by two mechanisms: merging of compatible paths and frustrated competition among incompatible ones. Together they drive the network through nucleation, growth, and freezing into multi-input, single-output directed inverse trees. The picture reproduces the training dynamics of a 1.5-billion-parameter LLM and yields three predictions: reasoning chains lengthen as a geometric necessity of sparse topology; SFT induces catastrophic forgetting through bridge-node rupture; and frustration drives policy collapse. Building on the structural timing inherent in inverse-tree freezing, we propose Annealed-RLVR -- a brief SFT intervention at the moment of maximum frustration. It outperforms standard RLVR on both in- and out-of-distribution benchmarks, with the largest gains at high sampling budgets where standard RLVR collapses. The same SFT applied after the trees freeze instead triggers catastrophic forgetting, isolating timing as the active ingredient.

cs.AI↗

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

Crossover Scaling of Binder Cumulant and its application in Non-reciprocal Sandpiles

In this letter, we unveil a robust, pre-asymptotic scaling regime for the Binder cumulant $U_L$, a central finite-size scaling tool, demonstrating $U_L\sim N^{-1} |t|^{-dν}$ (disordered phase) and $\frac{2}{3}-U_L\sim N^{-1} |t|^{-dν}$ (ordered phase), with $t$ being the reduced control parameter, and $N$, $d$, $ν$ represent the total number of sites, the dimensionality, and correlation length exponent, respectively. Leveraging this result, we resolve a fundamental question on the stability of universality classes under the breaking of microscopic reciprocity. For the conserved Manna sandpile, we show that reciprocal biases preserve its universality class, merely shifting the critical point. In striking contrast, any non-reciprocal interaction acts as a relevant perturbation, decisively driving the system's critical exponents to flow from their non-mean-field values towards the mean-field related ones. This flow establishes non-reciprocity as a generic mechanism inducing mean-field criticality in conserved, non-equilibrium systems.

cond-mat.stat-mech↗

arXiv2026

Self-similar Dynamics in Percolation and Sandpile

Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap -- the size increment of clusters upon bond addition -- and the corresponding merged cluster, we identify scale-invariant temporal patterns in both quantities throughout a large portion of the process. This reveals a form of temporal self-similarity that has not been reported before. We further establish quantitative relations between the dynamic scaling exponents and the conventional static critical exponents, which enable the determination of critical behavior without prior knowledge of the critical point. The same self-similar dynamics is observed in both bond and site percolation on lattices and networks, and extends to other systems such as explosive and rigidity percolation. Moreover, similar temporal scaling is found in the initial nonequilibrium evolution of the Bak-Tang-Wiesenfeld sandpile model, suggesting a dynamic critical behavior distinct from its equilibrium state. These results provide a unified framework for understanding critical dynamics and may find applications in a broad range of complex systems.

cond-mat.stat-mech↗

arXiv2026

Percolation in the three-dimensional Ising model

Geometric representations provide a useful perspective on critical phenomena in the Ising model. In a recent study [Phys. Rev. E 112, 034118 (2025)], we found that the two-dimensional critical Ising model exhibits two consecutive percolation transitions for geometric spin clusters as the bond-occupation probability $p$ between parallel spins increases. Here, through extensive Monte Carlo simulations, we show that this phenomenon does not persist in three dimensions, where we observe only a single percolation transition on critical Ising configurations. Further theoretical analysis of the Ising model on the complete graph also yields the same scenario. In addition, we study percolation on a two-dimensional layer embedded in the three-dimensional critical Ising model. For this layer system, we estimate the red-bond exponent $y_p = 0.426(6)$ and the fractal dimensions of the largest cluster, hull, and shortest path as $d_f = 1.8926(20)$, $d_{\rm hull} = 1.663(4)$, and $d_{\rm min} = 1.080(10)$, respectively. These values indicate a distinct universality class induced by coupling to out-of-plane critical correlations.

cond-mat.stat-mech↗

arXiv2026

Evolving fractal dimensions in iterative bicolored percolation

Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. We introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and transform fractal dimensions. Starting from critical configurations, such as the O$(n)$ loop and fuzzy Potts models, successive coarse-graining generates a hierarchy of distinct yet critical generations. Using the conformal loop ensemble, we derive exact, generation-dependent fractal dimensions, which are quantitatively confirmed by large-scale Monte Carlo simulations. The evolutionary trajectory depends not only on the universality class of the initial state but also on whether it possesses a two-state critical structure, leading to different critical exponents starting from site and bond percolation. These results establish a general geometric mechanism for evolving fractal dimensions, in which scale invariance persists across generations.

cond-mat.stat-mech↗