Self-Similarity Breaking: Anomalous Nonequilibrium Finite-Size Scaling and Finite-Time Scaling

Yuan, Weilun; Yin, Shuai; Zhong, Fan

doi:10.1088/0256-307x/38/2/026401

Cited by 7 publications

(38 citation statements)

References 53 publications

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“…1(d) and 1(e) around 𝑇c, though far away from it, the collapses are not quite good near the peaks where fluctuations are large as expected. [93,95] Similar results are obtained for 𝒯 = 15. [78] This is reasonable once the driven time is shorter than the cutoff memory time so that the latter becomes sub-leading.…”

supporting

confidence: 82%

“…[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%

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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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confidence: 82%

mentioning

confidence: 99%

Theory of Critical Phenomena with Memory

Zeng¹,

ping²,

Zhong³

2022

Chinese Phys. Lett.

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“…We now present the FTS of the entanglement entropy S in real-time driving. We will not consider effects of phase ordering [78], since it has been shown that once the extrinsic self-similarity of the so-called phases fluctuations is considered, critical scaling is good down to quite low temperatures [114,115]. In the real-time evolution, the correlation length does not converge and we cannot study its scaling unfortunately.…”

Section: B Fts With Finite Entanglementsmentioning

confidence: 99%

Scaling Theories of Kosterlitz-Thouless Phase Transitions

Zuo,

Yin,

Cao

et al. 2021

Preprint

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We propose scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their combinations are studied. Relaxation times of both a usual power-law and an unusual power-law with a logarithmic factor are considered. Finite-size and finite-entanglement scaling forms somehow similar to a frequently employed ansatz are presented. The Kibble-Zurek scaling of topological defect density for a linear driving across the KT transition point is investigated in detail. An implicit equation for a rate exponent in the theory is derived and the exponent varies with the distance from the critical point and the driving rate consistent with relevant experiments. To verify the theories, we utilize the KT phase transition of a one-dimensional Bose-Hubbard model. The infinite time-evolving-blockdecimation algorithm is employed to solve numerically the model for finite bond dimensions. Both a correlation length and an entanglement entropy in imaginary time and only the entanglement entropy in real-time driving are computed. Both the short-time critical dynamics in imaginary time and the finite-time scaling in real-time driving, both including the finite bond dimension, for the measured quantities are found to describe the numerical results quite well via surface collapses. The critical point is also estimated and confirmed to be 0.302(1) at the infinite bond dimension on the basis of the scaling form.

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“…Recently [86,87], through studying the whole driving dynamics and hence the whole scaling functions rather than just at the critical point of the 2D Ising model, we discovered that the FTS and the FSS of some observable quantities are violated either in heating or in cooling even in their respective FTS and FSS regimes. Such anomalous scaling were found to originate from a novel source, the extrinsic self-similarity breaking of the so-called phases fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Phases fluctuations and anomalous finite-time scaling in an externally applied field on finite-sized lattices

Yuan¹,

Zhong²

2021

J. Phys.: Condens. Matter

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We study in detail the dynamic scaling of the three-dimensional Ising model under cooling on finite-sized lattices subject to an externally applied field whose magnitude fixes a scaled variable pertinent to it. Three different protocols, protocols A, B, and C, in which the field is applied either only below or only above the critical point besides during the whole process, respectively, are investigated. Anomalous finite-time scaling (FTS) are found in protocols B and C on a large lattice only and in protocol A when extrinsic self-similarity is broken. However, these anomalous scalings in cooling can be rectified unexpectedly by the recently found breaking-of-extrinsic-self-similarity exponent of FTS in zero-field heating, except in the case of protocol B in which a reduced zero-field cooling exponent is additionally required. This provides a distinctive source to the breaking-of-extrinsic-self-similarity exponents and thus confirms their validity. The different scaling behaviors of the three different protocols also shows that the so-called phases fluctuations at and above the critical point are more important than those below it. The previously found qualitative difference between zero-field heating and zero-field cooling is essentially the symmetry of the system states, namely whether they are ordered or disordered. We also confirm that there exists a revised FTS regime-the regime in which both the lattice sizes and driving rates are indispensable-in between the two end regimes of FTS and finite-size scaling even in the presence of the field. Its crossover to the end FTS regime is responsible for the anomalous scalings of the large lattice size in protocols B and C. However, our results show that the revised FTS is never needed for the usual order parameter in which no absolute value is taken. In addition, the end FTS regime in cooling is found to exhibit a special feature different from that in heating. Our results demonstrate that new exponents are needed for scaling in the whole driven process even in the case in which an external field is applied.

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Self-Similarity Breaking: Anomalous Nonequilibrium Finite-Size Scaling and Finite-Time Scaling

Cited by 7 publications

References 53 publications

Theory of Critical Phenomena with Memory

Theory of Critical Phenomena with Memory

Scaling Theories of Kosterlitz-Thouless Phase Transitions

Phases fluctuations and anomalous finite-time scaling in an externally applied field on finite-sized lattices

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