Statistical Physics and Complex Systems
My research lies at the intersection of statistical physics and complex systems, where I investigate the emergent behavior of interacting systems through the lens of phase transitions and critical phenomena. By leveraging analytical and computational tools, I aim to uncover universal principles governing the collective dynamics of systems ranging from simple lattice models to intricate real-world networks.
Phase Transitions and Critical Phenomena
Phase transitions, where a system undergoes a qualitative change in its macroscopic properties, are a central theme in statistical physics. I am particularly interested in critical phenomena, which describe the universal behavior of systems near phase transitions. These phenomena are characterized by power-law scaling and critical exponents, which often transcend the microscopic details of the system. My work explores how these universal features arise in various models and how they can be harnessed to understand real-world systems.
Explosive Percolation
Explosive percolation has been widely shown to exhibit abnormal finite-size behaviors that deviate from the standard finite-size scaling theory, often misleadingly interpreted as discontinuous phase transitions. We developed a dynamic method, called the event-based ensemble, which reveals that explosive percolation still adheres to the standard finite-size scaling theory (PRL.130.147101). The observed anomalies arise from the mixing of finite-size behaviors due to the Gaussian distribution of the pseudocritical point over a wide range, potentially exceeding the critical finite-size window. These findings hold in any dimension (PRR.6.033319).
Crossover Finite-Size Scaling Theory
Understanding finite-size scaling in critical phenomena, particularly the transition from finite systems to the thermodynamic limit, remains a significant challenge. A key issue lies in reconciling the finite-size scaling behavior near pseudocritical points with the scaling observed in infinite systems at criticality. We established a comprehensive crossover finite-size scaling theory that provides a unified framework for addressing this challenge (arXiv:2412.06228). By analyzing the asymptotic behavior of scaled observables in the crossover regime, we identified a novel λ-dependent finite-size scaling when approaching the critical point in a regime extending beyond the finite-size critical window. This theory quantitatively explains the abnormal finite-size behaviors in explosive percolation and bridges the gap between Gaussian asymptotics and complete graph asymptotics observed in high-dimensional percolation. This work advances the understanding of finite-size effects and offers a powerful framework for studying critical phenomena in diverse systems, with broad implications for statistical mechanics, network theory, and beyond.
Iterative Percolation
Criticality is generally believed to be fragile, representing an unstable fixed point in the renormalization group flow. We proposed a model (PRR.6.033318) where, starting from a critical configuration, we randomly reassign the color (black or white) of each cluster and obtain coarse-grained configurations by merging adjacent clusters of the same color. This process can be infinitely iterated in the infinite-lattice limit, with the system remaining at criticality but exhibiting different critical exponents. Extensive simulations reveal a continuous family of previously unknown universalities through the generation-dependent fractal dimension.
In an earlier work, we introduced history-dependent percolation (NSR.7.1296), where the iteration process triggers cascading failures. Remarkably, this model exhibits a continuous phase transition for any finite number of iterations, while an infinite iteration limit leads to a discontinuous phase transition. This work highlights the intricate interplay between iteration dynamics and phase transition behavior, offering new insights into the robustness and fragility of critical systems.
Phase Transitions in Complex Networks
In complex networks, phase transitions manifest in phenomena such as the emergence of giant components, synchronization, and epidemic spreading. My research focuses on how network topology—such as degree distribution, clustering, and community structure—influences critical behavior. By bridging statistical physics and network science, I aim to uncover universal principles that govern phase transitions in both synthetic and real-world networks, such as social, biological, and technological systems.
Percolation on Complex Networks
Over the past two decades, network science has profoundly influenced fields such as statistical physics, computer science, biology, and sociology by providing insights into the heterogeneous interaction patterns of complex systems. As a paradigm for random and semi-random connectivity, percolation theory plays a pivotal role in the development of network science and its applications. The robustness of networked systems is a central issue in studying real-world complexity. Using percolation models, we have explored key concepts such as the emergence of giant clusters, finite-size scaling, and mean-field methods to quantify and solve core problems in network science. These insights have facilitated the understanding of networked systems, including robustness, epidemic spreading, vital node identification, and community detection. Simultaneously, network science has introduced new challenges to percolation theory, such as percolation in strongly heterogeneous systems, topological transitions beyond pairwise interactions, and the emergence of giant clusters with mutual connections. We have written a review article on this topic (PhysRep.907.1), encompassing our earlier works, and authored a book (《网络渗流》) providing a systematic introduction to the fundamentals of percolation theory on networks.
Dynamics in Networked Systems
The strong heterogeneity of real-world networks gives rise to novel and often unexpected phenomena in dynamical processes, challenging traditional theoretical frameworks. Our research focuses on understanding how network topology - such as degree distribution, clustering, and community structure — shapes the behavior of dynamical systems, including epidemic spreading, traffic flow, synchronization, and evolutionary games. By bridging statistical physics and network science, we aim to uncover universal principles that govern these dynamics and their critical transitions.