The phenomenon of "order from disorder" (OfD) represents a counter-intuitive paradigm in condensed matter physics and statistical mechanics, wherein thermal or quantum fluctuations lift the macroscopic degeneracy of a frustrated system, thereby stabilizing a specific long-range ordered state. This paper explores the algorithmic underpinning of this emergent reality, framing the selection mechanism as a "muse" that orchestrates structure out of chaotic potential. We examine the interplay between geometric frustration, such as that found in triangles-in-triangles lattices and pyrochlore structures, and the quantum mechanical forces that drive phase transitions. By synthesizing recent theoretical advances in quantum spin systems, double-exchange models, and lattice QCD, we propose a unified "Fluctuation-Topology-Entanglement" (FTE) framework. This framework aims to predict the specific ordered ground states selected by fluctuations in systems exhibiting fractal-like spectral properties or geometric complexity. We conclude that the algorithmic reality of OfD is not merely a statistical anomaly but a fundamental organizing principle of quantum matter, having profound implications for the design of novel magnetic materials and quantum information architectures.The phenomenon of "order from disorder" (OfD) represents a counter-intuitive paradigm in condensed matter physics and statistical mechanics, wherein thermal or quantum fluctuations lift the macroscopic degeneracy of a frustrated system, thereby stabilizing a specific long-range ordered state. This paper explores the algorithmic underpinning of this emergent reality, framing the selection mechanism as a "muse" that orchestrates structure out of chaotic potential. We examine the interplay between geometric frustration, such as that found in triangles-in-triangles lattices and pyrochlore structures, and the quantum mechanical forces that drive phase transitions. By synthesizing recent theoretical advances in quantum spin systems, double-exchange models, and lattice QCD, we propose a unified "Fluctuation-Topology-Entanglement" (FTE) framework. This framework aims to predict the specific ordered ground states selected by fluctuations in systems exhibiting fractal-like spectral properties or geometric complexity. We conclude that the algorithmic reality of OfD is not merely a statistical anomaly but a fundamental organizing principle of quantum matter, having profound implications for the design of novel magnetic materials and quantum information architectures.

Feb 18, 20260 citations

Criticality in correlated quantum matter

Angela Kopp, Sudip Chakravarty

arXiv:cond-mat/0503298Nature PhysicsSep 29, 2005122 citations

Studying line defect at Deconfined Quantum Criticality via fuzzy sphere regularization

Shutao Liu, Shuai Yang, Jie Lou +1 more

The interplay between bulk critical fluctuations and nontrivial topology can enrich defect physics and give rise to novel defect universality classes. Understanding the fate of such defects therefore constitutes an important open problem. In this work, we studied a particularly simple setting: a (0+1)-dimensional pinning-field defect coupled to a (2+1)-dimensional deconfined quantum critical bulk. Using the fuzzy-sphere regularization, we numerically investigated the defect operator spectrum and extracted several universal quantities characterizing the defect conformal fixed point, including the scaling dimensions of defect-changing(creating) operators and the defect $g$ -function. These results establish the first numerical characterization of line-defect conformal data at deconfined quantum criticality and may stimulate further investigations of defect critical phenomena in topological quantum critical matter.The interplay between bulk critical fluctuations and nontrivial topology can enrich defect physics and give rise to novel defect universality classes. Understanding the fate of such defects therefore constitutes an important open problem. In this work, we studied a particularly simple setting: a (0+1)-dimensional pinning-field defect coupled to a (2+1)-dimensional deconfined quantum critical bulk. Using the fuzzy-sphere regularization, we numerically investigated the defect operator spectrum and extracted several universal quantities characterizing the defect conformal fixed point, including the scaling dimensions of defect-changing(creating) operators and the defect $g$-function. These results establish the first numerical characterization of line-defect conformal data at deconfined quantum criticality and may stimulate further investigations of defect critical phenomena in topological quantum critical matter.

arXiv:2609.03465Sep 3, 20260 citations

Quantum criticality in the nonunitary dynamics of ( 2 + 1 ) -dimensional free fermions

Qicheng Tang, Xiao Dong Chen, W. Zhu

Quantum criticality, which exhibits universal features such as nontrivial collective fluctuations, is one of the central topics in statistical and condensed matter physics. Here, the authors design a class of nonunitary random dynamics of free fermions that robustly produces novel critical steady states. The emergent quantum criticality is numerically confirmed for the 2+1 dimensional case, and the proposed analytical interpretation can be easily extended to any dimensions. Their discoveries are potentially helpful to understand quantum critical phenomenon in nonequilibrium dynamics.Quantum criticality, which exhibits universal features such as nontrivial collective fluctuations, is one of the central topics in statistical and condensed matter physics. Here, the authors design a class of nonunitary random dynamics of free fermions that robustly produces novel critical steady states. The emergent quantum criticality is numerically confirmed for the 2+1 dimensional case, and the proposed analytical interpretation can be easily extended to any dimensions. Their discoveries are potentially helpful to understand quantum critical phenomenon in nonequilibrium dynamics.

arXiv:2101.04320Physical review. B./Physical review. BMay 12, 202165 citations

Quantum Statistical Microdynamics and Critical Phenomena

Robert Goodell Brown, Mikael Ciftan

Springer eBooksJan 1, 19910 citations

g

-function. These results establish the first numerical characterization of line-defect conformal data at deconfined quantum criticality and may stimulate further investigations of defect critical phenomena in topological quantum critical matter.