Scaling theory of the Kosterlitz-Thouless phase transition

Zuo, Zhi-Yao; Yin, Shuai; Cao, Xuanmin; Zhong, Fan

doi:10.1103/physrevb.104.214108

Cited by 8 publications

(3 citation statements)

References 116 publications

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“…[67] FTS has been successfully applied to many systems to efficiently study their equilibrium and nonequilibrium critical properties. [13,[67][68][69][80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98] Here, we change the temperature 𝑇 through 𝜏 = 𝑇 −𝑇c = 𝑅𝑡 ′ [70] and choose 𝑅 as a variable in place of 𝑡 ′ . Accordingly, Eq.…”

mentioning

confidence: 99%

Theory of Critical Phenomena with Memory

Zeng¹,

ping²,

Zhong³

2022

Chinese Phys. Lett.

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Memory is a ubiquitous characteristic of complex systems and critical phenomena are one of the most intriguing phenomena in nature. Here, we propose an Ising model with memory and develop a corresponding theory of critical phenomena with memory for complex systems and discovered a series of surprising novel results. We show that a naive theory of a usual Hamiltonian with a direct inclusion of a power-law decaying long-range temporal interaction violates radically a hyperscaling law for all spatial dimensions even at and below the upper critical dimension. This entails both indispensable consideration of the Hamiltonian for dynamics, rather than the usual practice of just focusing on the corresponding dynamic Lagrangian alone, and transformations that result in a correct theory in which space and time are inextricably interwoven, leading to an effective spatial dimension that repairs the hyperscaling law. The theory gives rise to a set of novel mean-field critical exponents, which are different from the usual Landau ones, as well as new universality classes. These exponents are verified by numerical simulations of the Ising model with memory in two and three spatial dimensions.

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mentioning

confidence: 99%

Theory of Critical Phenomena with Memory

Zeng¹,

ping²,

Zhong³

2022

Chinese Phys. Lett.

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“…( 4), since all of them are the fixed points of the initial states. In contrast, for other initial states with finite initial order parameter and initial correlations, these initial conditions should be included in the scaling form [90][91][92][93][94][95][96][97][98].…”

Section: Brief Review Of the Dynamic Scaling In J-q3 Modelmentioning

confidence: 99%

“…Recently, spurred by the remarkable experimental progresses in manipulating and detecting the nonequilibrium quantum process, the quantum critical dynamics has attracted intensive attention from both theoretical and experimental aspects [86][87][88][89]. Among these studies, it was shown that the scaling properties of the imaginary-time relaxation dynamics near quantum critical points resemble those in the classical short-time critical dynamics [90][91][92][93][94][95][96][97][98].…”

Section: Introductionmentioning

confidence: 99%

Dual dynamic scaling in deconfined quantum criticality

Shu,

Yin

2022

Preprint

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Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical point (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the J-Q3 model. In this work, we study the nonequilibrium imaginary-time relaxation dynamics in the J-Q2 model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point, but also investigate the breakdown and the vestige of the dual dynamic scaling when the tuning parameter is away from the critical point. We also discuss its possible experimental realizations in devices of quantum computers.

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Anomalous fractal scaling in two-dimensional electric networks

Zhang

Sahin

et al. 2023

Commun Phys

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Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a two-dimensional LC circuit network. We find this anomalous impedance contribution to sensitively depend on the number of nodes N in a curious erratic manner and experimentally demonstrate its robustness against perturbations from the contact and parasitic impedance of individual components. This impedance anomaly is traced back to a generalized resonance condition reminiscent of Harper’s equation for electronic lattice transport in a magnetic field, even though our circuit network does not involve magnetic translation symmetry. It exhibits an emergent fractal parametric structure of anomalous impedance peaks for different N that cannot be reconciled with a continuum theory and does not correspond to regular waveguide resonant behavior. This anomalous fractal scaling extends to the transport properties of generic systems described by a network Laplacian whenever a resonance frequency scale is simultaneously present.

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Scaling theory of the Kosterlitz-Thouless phase transition

Cited by 8 publications

References 116 publications

Theory of Critical Phenomena with Memory

Theory of Critical Phenomena with Memory

Dual dynamic scaling in deconfined quantum criticality

Anomalous fractal scaling in two-dimensional electric networks

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