Scaling at quantum phase transitions above the upper critical dimension

Langheld, Anja; Koziol, Jan Alexander; Adelhardt, Patrick; Kapfer, Sebastian C.; Schmidt, K. P.

doi:10.21468/scipostphys.13.4.088

Cited by 15 publications

(60 citation statements)

References 87 publications

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“…The crossover-scaling formula (12) and related preceding studies are reconciled by the scaling theory above the upper critical dimension [48,49]. Following this theory [49], we introduce the length scale…”

Section: Multi-criticality Around the Xx-symmetric Point η = 0: Small...mentioning

confidence: 79%

“…Around the threshold α * = 2/3 derived by the hyperscaling relation [1,48], there should appear notorious logarithmic corrections to scaling [23,50,51,52], which prevent us from investigating the transient behavior in detail. It would be tempting to subtract these scaling corrections [23] so as to look into the leading singularities clearly.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…As in the ordinary magnet, above the upper critical dimension α < α * , the exponents at α = α * continue to be realized through taking the thermodynamic limit. Moreover, the threshold α * = 2/3 is also derived [1,48] by inserting the above critical exponents into the hyperscaling relation. Therefore, the scaling theory (12) does not contradict these preceding results.…”

Section: Multi-criticality Around the Xx-symmetric Point η = 0: Small...mentioning

confidence: 99%

See 2 more Smart Citations

Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality

Nishiyama

2021

Eur. Phys. J. B

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The transverse-field XY spin chain with competing antiferromagnetic long-range interactions, J r ∝ 1/r α (r: distance between spins), and the exponent α was investigated numerically. The main concern is to clarify the character of the transversefield-driven phase transition for the small-α regime around the XX-symmetric point, η = 0 (η: XY -anisotropy parameter). To cope with the negative-sign problem, we employed the exact-diagonalization method, which enables us to evaluate the fidelity susceptibility χ F . Because the fidelity susceptibility does not assume any order parameter after a phase transition, it detects the multi-criticality around the XXsymmetric point in a systematic manner. As a preliminary survey, with η = 0.5 and α = 2 fixed, we made the scaling analysis of χ F . The scaling behavior of χ F shows that the transverse-field-driven phase transition belongs to the 2D-Ising universality class. Thereby, with the properly crossover-scaled η, the χ F data is cast into the crossover scaling formula for the small-α regime. The multi-critical exponents fed into the scaling formula are argued through referring to related studies.

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Section: Multi-criticality Around the Xx-symmetric Point η = 0: Small...mentioning

confidence: 79%

Section: Summary and Discussionmentioning

confidence: 99%

Section: Multi-criticality Around the Xx-symmetric Point η = 0: Small...mentioning

confidence: 99%

See 1 more Smart Citation

Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality

Nishiyama

2021

Eur. Phys. J. B

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“…The later predicts that the magnetic susceptibility diverges with the lattice size with an exponent ϙ𝛾/𝜈 = 𝑑/2. This theory has recently been extended to quantum phase transitions [11]. Despite some indications that the same finite-size scaling holds with free boundary conditions, the problem is not completely settled [2,12].…”

Section: Introductionmentioning

confidence: 99%

Finite-size scaling of the majority-voter model above the upper critical dimension

Chatelain¹

2023

Condens. Matter Phys.

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The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension d = 2 to 7 with periodic boundary conditions. The critical exponents associated to the finite-size scaling of the magnetic susceptibility are shown to be compatible with those of the Ising model. At dimension d = 4, the numerical data are compatible with the presence of multiplicative logarithmic corrections. For d ≥ 5, the estimates of the exponents are close to the prediction d/2 when taking into account the dangerous irrelevant variable at the Gaussian fixed point. Moreover, the universal values of the Binder cumulant are also compatible with those of the Ising model. This indicates that the upper critical dimension of the majority-voter model is not dc = 6 as claimed in the literature, but dc = 4 like the equilibrium Ising model.

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“…We revisit this question in the AF side of the LR interactions for TFIC where the breakdown of the Ising class in the critical ground state seems to be very different from what is established in the ferromagnetic (FM) counterpart [47][48][49][50][51][52][56][57][58]. Because an exact solution is not available, constructing the picture of how its criticality deviates from the Ising class as 𝛼 LR decreases relies primarily on the collection of numerical observations.…”

Section: Introductionmentioning

confidence: 99%

A study on graphic design for the production of tourist souvenirs in Gwangju, Jeollanam-do

Kim¹

2023

Korea Inst Des Res Soc

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Currently, tourism souvenirs in Gwangju, Jeollanam-do are developing in various ways. However, there are a number of problems, such as a uniform souvenir design that focuses on food and traditional elements that can be purchased anywhere in Korea, and a lack of products that reflect social design trends. Graphic design was produced by selecting 100 items, including the natural environment of Gwangju, buildings and cultural relics, famous festivals in Gwangju, and traditional patterns, for the production of tourist souvenirs in Gwangju. Utilizing 100 design proposals that have been produced, even products that are usable and easy to carry have been developed and proposed. Also, based on this, we intend to discover and nurture various elements of Gwangju City as elements that can commemorate and visit Gwangju City once again.

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Scaling at quantum phase transitions above the upper critical dimension

Cited by 15 publications

References 87 publications

Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality

Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality

Finite-size scaling of the majority-voter model above the upper critical dimension

A study on graphic design for the production of tourist souvenirs in Gwangju, Jeollanam-do

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