We explore synchronization transitions in a generalized Kuramoto model with n-dimensional vector oscillators on complete graphs (CG) and on d-dimensional lattices. On the CG, we analytically derive universal critical exponents (β,ν[over ¯])=(1/2,5/2) for all even n. Through the Botet-Jullien-Pfeuty relation, the CG exponent ν[over ¯]=5/2 predicts an upper critical dimension d_{u}=5 for the corresponding lattice models. For locally coupled systems with d<d_{u}, we identify frequency entrainment for arbitrary n using a newly developed entrainment connectivity matrix, and characterize the transitions with two complementary order parameters. Using spin-wave theory together with numerical simulations, we obtain critical exponents across the (n,d) parameter space. These results suggest a family of n-independent but d-dependent universality classes, offering a unified perspective on how symmetry and dimensionality shape synchronization phenomena.
We investigate the hierarchical bifurcation and fixed-point structure of discrete-time dynamical systems arising from the q-state asymmetric Potts model on a Cayley tree of order k=2. For arbitrary q⩾3, the model reduces to a d=q−1-dimensional rational map. We derive a universal quadratic equation governing the fixed p...
We investigate quantum criticality in the transverse-field Ising model on finite Cayley trees and demonstrate that their extensive boundary fundamentally changes the nature of the quantum phase transition compared with the infinite, boundary-free Bethe lattice. Using tree tensor-network simulations for systems with up...
We propose that, at criticality, equilibrium dynamics effectively evolves on a fractal subspace rather than throughout the full Euclidean space. Starting from Fisher's formulation of the order-parameter correlation function, we interpret the anomalous critical exponent $\eta$ geometrically through a correlation fractal...
We investigate the relation between two complementary descriptions of the Anderson transition on small-world random graphs: finite-size scaling of eigenfunction moments and renormalization-group (RG) flows of multifractal dimensions $D_q$. The RG flows recover the qualitative structure previously reported for the infor...
Ignacio García-Mata, Wei-Tao Chen, John Martin et al.· 0 citations
We study the dynamical scaling properties of the two-dimensional fully frustrated Ising model by simulated annealing. The model has a highly degenerate, critical ground state with well known equilibrium properties. To study its out-of-equilibrium behavior, we develop an annealing protocol that is convenient for extendi...
We study the two-dimensional anisotropic three-state Potts ferromagnet on the square lattice using Wolff single-cluster Monte Carlo simulations and finite-size scaling. For coupling ratios $\lambda=J_y/J_x=0.5$, $0.75$, and $1$, finite-size scaling of the correlation ratio yields critical behavior consistent with the t...
Fan Yang, Jian Gao, Lu Liu et al.· 0 citations
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