Stability of critical behaviour, critical-exponent renormalization and first-order transitions

Capel, H.W.; Ouden, L.W.J. den; Perk, Jacques H. H.

doi:10.1016/0378-4371(79)90024-4

Cited by 24 publications

(10 citation statements)

References 54 publications

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“…This result confirms relation (14), and it agrees with the results in Sec. 6.4 in the paper by Capel, den Ouden, and Perk, 14 in which the scaling form for the free energy under perturbations is given for general cases.…”

Section: B Dependence Of the Critical Temperature On αsupporting

confidence: 93%

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Crossover between a short-range and a long-range Ising model

et al. 2011

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Recently, it has been found that an effective long-range interaction is realized among local bistable variables (spins) in systems where the elastic interaction causes ordering of the spins. In such systems, we generally expect both long-range and short-range interactions to exist. In the short-range Ising model, the correlation length diverges at the critical point. In contrast, in the long-range interacting model the spin configuration is always uniform and the correlation length is zero. As long as a system has nonzero long-range interactions, it shows criticality in the mean-field universality class, and the spin configuration is uniform beyond a certain scale. Here we study the crossover from the pure short-range interacting model to the long-range interacting model. We investigate the infinite-range model (Husimi-Temperley model) as a prototype of this competition, and we study how the critical temperature changes as a function of the strength of the long-range interaction. This model can also be interpreted as an approximation for the Ising model on a small-world network. We derive a formula for the critical temperature as a function of the strength of the long-range interaction. We also propose a finite-size scaling form for the spin correlation length at the critical point, which is finite as long as the long-range interaction is included, though it diverges in the limit of the pure short-range model. These properties are confirmed by extensive Monte Carlo simulations.

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Section: B Dependence Of the Critical Temperature On αsupporting

confidence: 93%

“…6.4 in the paper by Capel, den Ouden, and Perk, 14 in which the scaling form for the free energy under perturbations is given for general cases. This scaling property is also obtained in Hastings' paper.…”

Section: B Dependence Of the Critical Temperature On αmentioning

confidence: 99%

Crossover between a short-range and a long-range Ising model

et al. 2011

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“…Let us stress that this non-local mapping does not keep track of state properties as well as degeneracies. However, the QTFIM and its dual are isospectral and we can therefore directly conclude that also H QTFIM dual displays a first-order phase transition in the thermodynamic limit, but in this case between a symmetry unbroken phase with zero magnetization per spin and zero photons per spin at small g and an ordered phase with finite M z and n for large g. These findings are indeed in accordance with general considerations of Rabi Hamiltonians competing with short-range interactions [38,39].…”

Section: Phase Diagramsupporting

confidence: 87%

The Ising model in a light-induced quantized transverse field

Rohn,

Hörmann,

Genes

et al. 2020

Preprint

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We investigate the influence of light-matter interactions on correlated quantum matter by studying the paradigmatic Ising model subject to a quantum Rabi coupling. This type of coupling to a confined, spatially delocalized bosonic light mode, such as provided by an optical resonator, resembles a quantized transverse magnetic field of tunable strength. As a consequence, the symmetry-broken magnetic state breaks down for strong enough light-mater interactions to a paramagnetic state. The non-local character of the bosonic mode can change the quantum phase transition in a drastic manner, which we analyze quantitatively for the simplest case of a chain geometry (Dicke-Ising chain). The results show a direct transition between a magnetically ordered phase with zero photon density and a magnetically polarized phase with lasing behaviour of the light. Our predictions are equally valid for the dual quantized Ising chain in a conventional transverse magnetic field.

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“…Because of their continued academic importance and relevance to real systems, phase transitions in constrained systems remained a focus of study [5][6][7][8][9]. In recent years the transformation has been extended to deal with other aspects of critical phenomena [10,11].…”

Section: Introductionmentioning

confidence: 99%

Critical phenomena for systems under constraint

Измаилян¹,

Kenna²

2014

Condens. Matter Phys.

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It is well known that the imposition of a constraint can transform the properties of critical systems. Early work on this phemomenon by Essam and Garelick, Fisher, and others, focused on the effects of constraints on the leading critical exponents describing phase transitions. Recent work extended these considerations to critical amplitudes and to exponents governing logarithmic corrections in certain marginal scenarios. Here these old and new results are gathered and summarised. The involutory nature of transformations between the critical parameters describing ideal and constrained systems are also discussed, paying particular attention to matters relating to universality.

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Stability of critical behaviour, critical-exponent renormalization and first-order transitions

Cited by 24 publications

References 54 publications

Crossover between a short-range and a long-range Ising model

Crossover between a short-range and a long-range Ising model

The Ising model in a light-induced quantized transverse field

Critical phenomena for systems under constraint

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