Erratum to: Monotonicity of Ursell functions in the Ising model
In this note, we correct an error in the proof Theorem 1 of Comm. Math. Phys. 401 (2023), 2459-2482.
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arXiv subjects
Jianping Jiang
Publications and source records attributed to Jianping Jiang.
A connection inequality for the random-cluster model
For a finite graph $G=(V,E)$, let $ϕ$ be the random-cluster measure with edge parameters $(p_e)_{e\in E}$, cluster weight $q\geq 1$ and free boundary condition. For each $x\in V$ and all nonempty $A,B\subseteq V$, we prove $ϕ(x\leftrightarrow B)\geq ϕ(x\leftrightarrow A)\min_{a\in A}ϕ(a\leftrightarrow B)$. For $q=1$, this is the (slightly generalized) Kozma-Nitzan inequality. Our extension to $q>1$ is based on a recent proof of this inequality by Blanc-Renaudie. As an application, we give a simple proof of sharp upper bounds for one-arm and point-to-plane connection probabilities in the subcritical regime.
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Phase transition in the antiferromagnetic Ising model with external field
Consider the nearest-neighbor antiferromagnetic Ising model on $\mathbb{Z}^d$, $d\ge2$, at inverse temperature $β$ and in a uniform external field $h$. Let $β_c(d)$ be the critical inverse temperature of the zero-field Ising model. We prove that for every $β>β_c(d)$, the Gibbs state is not unique whenever $|h|$ is sufficiently small. This extends a previous result of Dobrushin (1968) from sufficiently large $β$ to every $β>β_c(d)$.
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Coexistence of infinite clusters for percolation and Ising model on $\mathbb{Z}^d$
For independent bond percolation on $\mathbb{Z}^d$ with parameter $p$, let $p_c^b(d)$ be the critical probability. We prove that for each $d \geq 9$, there is $ε_d>0$ such that for each $p \in (p_c^b(d), p_c^b(d)+ε_d)$, the complement of the infinite open cluster stochastically dominates a supercritical site percolation on $\mathbb{Z}^d$. This improves the previous results by Grimmett, Holroyd and Kozma 2014, and Bock, Damron, Newman and Sidoravicius 2020. Numerical estimates of $p_c^b(d)$ and $p_c^s(d)$ (the site critical probability) suggest that a similar stochastic domination result holds for all $d \geq 4$. For the Ising model on $\mathbb{Z}^d$ with inverse temperature $β$, let $β_c(d)$ be the critical inverse temperature. We prove that for each $d \geq 8$, there is $ε_d>0$ such that for each $β\in [0,β_c(d)+ε_d)$, the $+$ spins under the minus phase stochastically dominate a supercritical site percolation on $\mathbb{Z}^d$. This improves the previous result of Aizenman, Bricmont and Lebowitz 1987. Numerical estimates of $β_c(d)$ and $p_c^s(d)$ suggest that a similar stochastic domination result holds for all $d \geq 5$.
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A simple proof of exponential decay for the near-critical planar Ising model
For the Ising model defined on $a\mathbb{Z}^2$ at critical temperature with external field $a^{15/8}h$, we give a simple and elementary proof that its truncated two-point function decays exponentially. The proof combines the high temperature expansion, random-cluster and random current representations. A new input in the proof is that, in the near-critical sourceless single current measure, there are many loops formed by a path on $a\mathbb{Z}^2$ with diameter of order $1$, together with two external edges that connect the path's endpoints to the ghost.
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A General Coupling for Ising Models and Beyond
The couplings between the Ising model and its graphical representations, the random-cluster, random current and loop $\mathrm{O}(1)$ models, are put on common footing through a generalization of the Swendsen-Wang-Edwards-Sokal coupling. A new special case is that the single random current with parameter $2J$ on edges of agreement of XOR-Ising spins has the law of the double random current. The coupling also yields a general mechanism for constructing conditional Bernoulli percolation measures via uniform sampling, providing new perspectives on models such as the arboreal gas, random $d$-regular graphs, and self-avoiding walks. As an application of the coupling for the Loop-Cluster joint model, we prove that the regimes of exponential decay of the $q$-state Potts model, the random-cluster representation, and its $q$-flow loop representation coincide on the torus, generalizing the Ising result. By providing a new and equivalent definition of the plaquette random cluster model, we are able to generalize the loop-cluster coupling to lattice gauge theories.
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The free state for the Potts model on Cayley trees is either extremal or glassy
For the Potts model on the Cayley tree $\mathbb{T}^d$ with branching factor $d\geq 2$, we consider the free state which is obtained as the limiting Gibbs measure with free boundary conditions. We prove that the free state is either extremal or glassy (i.e., whose decomposition into extremal Gibbs measures contains uncountably many components). As a corollary, the free state for the Ising model on $\mathbb{T}^d$ is glassy if and only if the inverse temperature $β>\operatorname{arctanh}(1/\sqrt{d})$; this generalizes a previous result by Gandolfo, Maes, Ruiz and Shlosman (2020) from a very low temperature regime to the entire spin-glass regime.
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CCCL: Node-Spanning GPU Collectives with CXL Memory Pooling
Large language models (LLMs) training or inference across multiple nodes introduces significant pressure on GPU memory and interconnect bandwidth. The Compute Express Link (CXL) shared memory pool offers a scalable solution by enabling memory sharing across nodes, reducing over-provisioning and improving resource utilization. We propose \name, a collective communication library, leveraging the CXL shared memory pool to support cross-node GPU operations without relying on traditional RDMA-based networking. Our design addresses the challenges on synchronization, data interleaving, and communication parallelization faced by using the CXL shared memory pool for collective communications. Evaluating on multiple nodes with a TITAN-II CXL switch and six Micron CZ120 memory cards, we show that \name achieves highly efficient collective operations across hosts, demonstrating CXL's potential for scalable, memory-centric GPU communication. Our evaluation demonstrates that \name achieves average performance improvements of 1.34$\times$ for AllGather, 1.84$\times$ for Broadcast, 1.94$\times$ for Gather, and 1.04$\times$ for Scatter, compared to the original RDMA-based implementation over 200 Gbps InfiniBand. \textcolor{dong}{In addition, the evaluation with a case of LLM training shows 1.11$\times$ speedup compared with the InfiniBand while saving production cost by $2.75\times$ in hardware.}
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Ming-Flash-Omni: A Sparse, Unified Architecture for Multimodal Perception and Generation
We propose Ming-Flash-Omni, an upgraded version of Ming-Omni, built upon a sparser Mixture-of-Experts (MoE) variant of Ling-Flash-2.0 with 100 billion total parameters, of which only 6.1 billion are active per token. This architecture enables highly efficient scaling (dramatically improving computational efficiency while significantly expanding model capacity) and empowers stronger unified multimodal intelligence across vision, speech, and language, representing a key step toward Artificial General Intelligence (AGI). Compared to its predecessor, the upgraded version exhibits substantial improvements across multimodal understanding and generation. Notably, it achieves strong performance on vision-language understanding benchmarks, with overall scores on par with Gemini 2.5 Pro, and enables seamless switching among multimodal tasks in multi-turn interactions. In speech, it achieves strong performance in contextual and dialect-aware ASR while enabling joint, continuous-generation of speech, sound, and music. In vision, it introduces generative semantic segmentation that achieves competitive standalone performance and enhances spatial control and editing consistency, alongside marked improvements in identity preservation, and high-fidelity in-image text rendering. Together, these capabilities demonstrate that a single unified model can serve as a practical foundation for general-purpose multimodal intelligence.
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Percolation of both signs in a triangular-type 3D Ising model above $T_c$
Let $\mathbb{T}$ be the two-dimensional triangular lattice, and $\mathbb{Z}$ the one-dimensional integer lattice. Let $\mathbb{T}\times \mathbb{Z}$ denote the Cartesian product graph. Consider the Ising model defined on this graph with inverse temperature $β$ and external field $h$, and let $β_c$ be the critical inverse temperature when $h=0$. We prove that for each $β\in[0,β_c)$, there exists $h_c(β)>0$ such that both a unique infinite $+$cluster and a unique infinite $-$cluster coexist whenever $|h|<h_c(β)$. The same coexistence result also holds for the three-dimensional triangular lattice.
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SOLAMI: Social Vision-Language-Action Modeling for Immersive Interaction with 3D Autonomous Characters
Human beings are social animals. How to equip 3D autonomous characters with similar social intelligence that can perceive, understand and interact with humans remains an open yet foundamental problem. In this paper, we introduce SOLAMI, the first end-to-end Social vision-Language-Action (VLA) Modeling framework for Immersive interaction with 3D autonomous characters. Specifically, SOLAMI builds 3D autonomous characters from three aspects: (1) Social VLA Architecture: We propose a unified social VLA framework to generate multimodal response (speech and motion) based on the user's multimodal input to drive the character for social interaction. (2) Interactive Multimodal Data: We present SynMSI, a synthetic multimodal social interaction dataset generated by an automatic pipeline using only existing motion datasets to address the issue of data scarcity. (3) Immersive VR Interface: We develop a VR interface that enables users to immersively interact with these characters driven by various architectures. Extensive quantitative experiments and user studies demonstrate that our framework leads to more precise and natural character responses (in both speech and motion) that align with user expectations with lower latency.
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Random walk on dynamical percolation in Euclidean lattices: separating critical and supercritical regimes
We study the random walk on dynamical percolation of $\mathbb{Z}^d$ (resp., the two-dimensional triangular lattice $\mathcal{T}$), where each edge (resp., each site) can be either open or closed, refreshing its status at rate $μ\in (0,1/e]$. The random walk moves along open edges in $\mathbb{Z}^d$ (resp., open sites in $\mathcal{T}$) at rate $1$. For the critical regime $p=p_c$, we prove the following two results: on $\mathcal{T}$, the mean squared displacement of the random walk from $0$ to $t$ is at most $O(tμ^{5/132-ε})$ for any $ε>0$; on $\mathbb{Z}^d$ with $d\geq 11$, the corresponding upper bound for the mean squared displacement is $O(t μ^{1/2}\log(1/μ))$. For the supercritical regime $p>p_c$, we prove that the mean squared displacement on $\mathbb{Z}^d$ is at least $ct$ for some $c=c(d)>0$ that does not depend on $μ$.
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Speed of random walk on dynamical percolation in nonamenable transitive graphs
Let $G$ be a nonamenable transitive unimodular graph. In dynamical percolation, every edge in $G$ refreshes its status at rate $μ>0$, and following the refresh, each edge is open independently with probability $p$. The random walk traverses $G$ only along open edges, moving at rate $1$. In the critical regime $p=p_c$, we prove that the speed of the random walk is at most $O(\sqrt{μ\log(1/μ)})$, provided that $μ\le e^{-1}$. In the supercritical regime $p>p_c$, we prove that the speed on $G$ is of order 1 (uniformly in $μ)$, while in the subcritical regime $p<p_c$, the speed is of order $μ\wedge 1$.
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Complementing Event Streams and RGB Frames for Hand Mesh Reconstruction
Reliable hand mesh reconstruction (HMR) from commonly-used color and depth sensors is challenging especially under scenarios with varied illuminations and fast motions. Event camera is a highly promising alternative for its high dynamic range and dense temporal resolution properties, but it lacks key texture appearance for hand mesh reconstruction. In this paper, we propose EvRGBHand -- the first approach for 3D hand mesh reconstruction with an event camera and an RGB camera compensating for each other. By fusing two modalities of data across time, space, and information dimensions,EvRGBHand can tackle overexposure and motion blur issues in RGB-based HMR and foreground scarcity and background overflow issues in event-based HMR. We further propose EvRGBDegrader, which allows our model to generalize effectively in challenging scenes, even when trained solely on standard scenes, thus reducing data acquisition costs. Experiments on real-world data demonstrate that EvRGBHand can effectively solve the challenging issues when using either type of camera alone via retaining the merits of both, and shows the potential of generalization to outdoor scenes and another type of event camera.
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EvHandPose: Event-based 3D Hand Pose Estimation with Sparse Supervision
Event camera shows great potential in 3D hand pose estimation, especially addressing the challenges of fast motion and high dynamic range in a low-power way. However, due to the asynchronous differential imaging mechanism, it is challenging to design event representation to encode hand motion information especially when the hands are not moving (causing motion ambiguity), and it is infeasible to fully annotate the temporally dense event stream. In this paper, we propose EvHandPose with novel hand flow representations in Event-to-Pose module for accurate hand pose estimation and alleviating the motion ambiguity issue. To solve the problem under sparse annotation, we design contrast maximization and hand-edge constraints in Pose-to-IWE (Image with Warped Events) module and formulate EvHandPose in a weakly-supervision framework. We further build EvRealHands, the first large-scale real-world event-based hand pose dataset on several challenging scenes to bridge the real-synthetic domain gap. Experiments on EvRealHands demonstrate that EvHandPose outperforms previous event-based methods under all evaluation scenes, achieves accurate and stable hand pose estimation with high temporal resolution in fast motion and strong light scenes compared with RGB-based methods, generalizes well to outdoor scenes and another type of event camera, and shows the potential for the hand gesture recognition task.
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EvPlug: Learn a Plug-and-Play Module for Event and Image Fusion
Event cameras and RGB cameras exhibit complementary characteristics in imaging: the former possesses high dynamic range (HDR) and high temporal resolution, while the latter provides rich texture and color information. This makes the integration of event cameras into middle- and high-level RGB-based vision tasks highly promising. However, challenges arise in multi-modal fusion, data annotation, and model architecture design. In this paper, we propose EvPlug, which learns a plug-and-play event and image fusion module from the supervision of the existing RGB-based model. The learned fusion module integrates event streams with image features in the form of a plug-in, endowing the RGB-based model to be robust to HDR and fast motion scenes while enabling high temporal resolution inference. Our method only requires unlabeled event-image pairs (no pixel-wise alignment required) and does not alter the structure or weights of the RGB-based model. We demonstrate the superiority of EvPlug in several vision tasks such as object detection, semantic segmentation, and 3D hand pose estimation
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Digital Life Project: Autonomous 3D Characters with Social Intelligence
In this work, we present Digital Life Project, a framework utilizing language as the universal medium to build autonomous 3D characters, who are capable of engaging in social interactions and expressing with articulated body motions, thereby simulating life in a digital environment. Our framework comprises two primary components: 1) SocioMind: a meticulously crafted digital brain that models personalities with systematic few-shot exemplars, incorporates a reflection process based on psychology principles, and emulates autonomy by initiating dialogue topics; 2) MoMat-MoGen: a text-driven motion synthesis paradigm for controlling the character's digital body. It integrates motion matching, a proven industry technique to ensure motion quality, with cutting-edge advancements in motion generation for diversity. Extensive experiments demonstrate that each module achieves state-of-the-art performance in its respective domain. Collectively, they enable virtual characters to initiate and sustain dialogues autonomously, while evolving their socio-psychological states. Concurrently, these characters can perform contextually relevant bodily movements. Additionally, a motion captioning module further allows the virtual character to recognize and appropriately respond to human players' actions. Homepage: https://digital-life-project.com/
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Monotonicity of Ursell functions in the Ising model
In this paper, we consider Ising models with ferromagnetic pair interactions. We prove that the Ursell functions $u_{2k}$ satisfy: $(-1)^{k-1}u_{2k}$ is increasing in each interaction. As an application, we prove a 1983 conjecture by Nishimori and Griffiths about the partition function of the Ising model with complex external field $h$: its closest zero to the origin (in the variable $h$) moves towards the origin as an arbitrary interaction increases.
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