This work introduces a complementary framework for analyzing critical transitions through transition accessibility rather than occupancy statistics alone. Using the two-dimensional Ising model as a test system, the study defines constraint density as a normalized measure of local transition entropy, quantifying the rigidity or flexibility of a system’s accessible transformation structure. Rather than proposing new physics or a new universality class, the framework explores whether accessibility-sensitive observables exhibit distinct restructuring morphology near standard critical transitions. Preliminary finite-size analyses suggest broader restructuring envelopes, extended response behavior, and distinct integrated susceptibility characteristics compared with canonical occupancy-sensitive observables. The work is exploratory and emphasizes observable restructuring topology rather than modifications to underlying dynamics. Potential applications include finite, noisy, or operationally constrained systems where broad restructuring behavior may be more informative than sharply localized critical coordinates.
This work introduces a complementary framework for analyzing critical transitions through transition accessibility rather than occupancy statistics alone. Using the two-dimensional Ising model as a test system, the study defines constraint density as a normalized measure of local transition entropy, quantifying the rigidity or flexibility of a system’s accessible transformation structure. Rather than proposing new physics or a new universality class, the framework explores whether accessibility-sensitive observables exhibit distinct restructuring morphology near standard critical transitions. Preliminary finite-size analyses suggest broader restructuring envelopes, extended response behavior, and distinct integrated susceptibility characteristics compared with canonical occupancy-sensitive observables. The work is exploratory and emphasizes observable restructuring topology rather than modifications to underlying dynamics. Potential applications include finite, noisy, or operationally constrained systems where broad restructuring behavior may be more informative than sharply localized critical coordinates.
While phases and phase transitions are conventionally described by local order parameters in real space, we present a unified framework characterizing the phase transition through the geometry of configuration space defined by the statistics of pairwise distances rH between configurations. Focusing on the concrete example of Ising spins, we establish crucial analytical links between this geometry and fundamental real-space observables, i.e., the magnetization and two-point spin correlation functions. This link unveils the universal scaling law in the configuration space: the standard deviation of the normalized distances exhibits universal criticality as Var(rH)∼L−2β/ν, provided that the system possesses zero magnetization and satisfies 4β/ν<d. We validate this scaling with stochastic series expansion quantum Monte Carlo simulations of the transverse-field Ising model(TFIM). Furthermore, we propose configuration-space diagnostics that go beyond local real-space observables. First, the distribution probability P(rH) parameterized by the transverse field h forms a one-dimensional manifold. Information-geometric analyses, particularly the Fisher information defined on this manifold, successfully pinpoint the TFIM phase transition, regardless of the measurement basis. Second, for the Su-Schrieffer-Heeger Heisenberg model, a parity index derived from P(rH) successfully characterizes the symmetry-protected topological phase and its transition. Our work establishes configuration space geometry as a novel perspective on quantum criticality, revealing how macroscopic universal phenomena are encoded within its global statistical features.
Uncovering and understanding universal dynamics in matter far from equilibrium remains a key challenge. In this work, we identify a so far unrecognized form of universal behavior that emerges after a sudden symmetry-breaking quench at continuous phase transitions. Our key observation is that the order-parameter fluctuations in Ising models exhibit a compelling temporal collapse across a wide range of system sizes and quench strengths, indicative of an emergent single-variable scaling form. This phenomenon can be explained by introducing a so far unknown dynamical critical exponent for the underlying continuous phase transition. We find evidence for a lower critical effective dimension of this universal regime: it is observed in the 2D quantum and 3D and 4D classical Ising models, but not in the 1D quantum or 2D classical cases. Our results suggest that our observed universal far-from-equilibrium scaling may extend beyond the Ising models studied here and could more broadly characterize systems with non-conserved order parameters, opening new avenues for exploring universal dynamics both theoretically and in current experimental platforms.
Phase transitions represent fundamental transformations of matter, characterized by abrupt changes in macroscopic properties and often associated with singular behavior at critical points. While equilibrium aspects of phase transitions, particularly universal critical exponents and scaling laws, are well-understood, the non-equilibrium processes occurring near criticality, especially the production of entropy, remain a rich area of investigation. This paper explores the intricate relationship between critical entropy production and the emergence of scaling laws in systems undergoing phase transitions. We delve into how the rate of entropy production diverges or exhibits anomalous scaling near critical points, reflecting the system's attempts to dissipate energy and respond to external perturbations as it approaches a state of macroscopic change. By integrating concepts from non-equilibrium thermodynamics, statistical mechanics, and renormalization group theory, we aim to elucidate the underlying mechanisms that govern entropy generation in these critical regimes. We discuss theoretical frameworks that predict universal scaling behaviors for entropy production rates, analogous to those observed for equilibrium order parameters and susceptibilities. The implications of these scaling laws extend beyond theoretical physics, offering insights into complex systems, far-from-equilibrium dynamics, and the efficiency of energy conversion processes in critical environments. Our analysis highlights the critical entropy production as a unique signature of non-equilibrium dynamics during phase transitions, providing a deeper understanding of the interplay between fluctuations, dissipation, and universality near points of instability.
We investigate the dynamical spin and charge susceptibilities and the associated quantum Fisher information in a class of interacting lattice models, with a primary focus on the Su-Schrieffer-Heeger model in the presence of Hatsugai-Kohmoto interactions. To provide a rigorous analytical benchmark, we contrast the response properties of the SSH-HK system with those of the single-band Hubbard and SSH-Hubbard models, treated within the random-phase approximation. While standard Hubbard-type interactions typically suppress excitation strength, we demonstrate that the SSH-HK model displays qualitatively distinct physical behavior arising from the interplay between SSH dimerization and the momentum-diagonal nature of the HK interaction. Leveraging the exact solvability of the HK term, we derive closed-form expressions for the dynamical susceptibility, revealing unique filling-controlled characteristics such as a finite response at zero wave vector and a pronounced restructuring of spectral weight across integer and fractional filling sectors. We show that the quantum Fisher information, defined as the frequency integral of the imaginary part of the susceptibility, serves as an efficient probe of these filling sectors, exhibiting distinct piecewise behavior that distinguishes integer from fractional fillings. Notably, our results indicate that the quantum Fisher information remains insensitive to topological transitions within uniform-density regimes, highlighting the limitations of standard dynamical response functions in characterizing band topology. These findings establish the SSH-HK model as a powerful analytical platform for exploring the competition between topology and strong correlations, demonstrating how dynamical susceptibilities and the quantum Fisher information provide complementary, experimentally accessible probes of many-body physics.