arXiv subjects

Li-Ru Zhang

Publications and source records attributed to Li-Ru Zhang.

3 recordsLinked to original sources

arXiv2025

Kinetic energy in random recurrent neural networks

High-dimensional chaotic dynamics can emerge in a large random recurrent neural network when the synaptic gain crosses a threshold. Recent works showed that the kinetic energy of neural activity links the chaotic dynamics and the supporting unstable fixed points (equilibria) in the phase space. Here, we investigate the kinetic-energy-centric properties of random recurrent neural networks by combining dynamical mean-field theory with extensive numerical simulations. We find that the average kinetic energy shifts continuously from zero to a positive value at the known critical value of coupling variance (synaptic gain) and exhibits a cubic scaling behavior near the critical point from above. This scaling behavior is supported by numerical simulations and provides a quantitative characterization of how fast the dynamics change during the onset of chaos as well as how far the chaotic dynamics are away from the unstable fixed points. The steady-state activity distribution is further calculated by the theory and compared with simulations on finite-size systems from the kinetic-energy optimization perspective as well. The activity distribution is also analyzed in a geometric angle, revealing that although the original chaotic dynamics and the gradient dynamics of the kinetic energy are arranged in a shell-like structure, they are well separated in the polar direction. The trajectory length on the chaotic manifold can be derived from the stationary kinetic energy, and the associated stationary behavior is analyzed as well.

cond-mat.stat-mech↗

arXiv2023

Sublattice extraordinary-log phase and new special point of the antiferromagnetic Potts model

We study the surface criticality of a three-dimensional classical antiferromagnetic Potts model, whose bulk critical behaviors belongs to the XY model because of emergent O(2) symmetry. We find that the surface antiferromagnetic next-nearest neighboring interactions can drive the extraordinary-log phase to the ordinary phase, the transition between the two phases belongs to the universality class of the well-known special transition of the XY model. Further strengthening the surface next-nearest neighboring interactions, the extraordinary-log phase reappears, but the main critical behaviors are dominated on the sublattices of the model; the special point between the ordinary phase and the sublattice extraordinary-log phase belongs to a new universality class.

cond-mat.stat-mech↗

arXiv2022

Surface criticality of antiferromagnetic Potts model

We study the three-state antiferromagnetic Potts model on the simple-cubic lattice, paying attention to the surface critical behaviors. When the nearest neighboring interactions of the surface is tuned, we obtain a phase diagram similar to the XY model, owing to the emergent O(2) symmetry of the bulk critical point. For the ordinary transition, we get $y_{h1}=0.780(3)$, $\eta_\parallel=1.44(1)$, and $\eta_\perp=0.736(6)$; for the special transition, we get $y_s=0.59(1)$, $y_{h1}=1.693(2)$, $\eta_\parallel=-0.391(4)$, and $\eta_\perp=-0.179(5)$; in the extraordinary-log phase, the surface correlation function $C_\parallel(r)$ decays logarithmically, with decaying exponent $q=0.60(2)$, however, the correlation $C_\perp(r)$ still decays algebraically, with critical exponent $\eta_\perp=-0.442(5)$. If the ferromagnetic next nearest neighboring surface interactions are added, we find two transition points, the first one is a special point between the ordinary phase and the extraordinary-log phase, the second one is a transition between the extraordinary-log phase and the $Z_6$ symmetry-breaking phase, with critical exponent $y_{\rm s}=0.41(2)$. The scaling behaviors of the second transition is very interesting, the surface spin correlation function $C_\parallel(r)$ and the surface squared staggered magnetization at this point decays logarithmically, with exponent $q=0.37(1)$; however, the surface structure factor with the smallest wave vector and the correlation function $C_\perp(r)$ satisfy power-law decaying, with critical exponents $\eta_\parallel=-0.69(1)$ and $\eta_\perp=-0.37(1)$, respectively.

cond-mat.stat-mech↗