Critical-exponent renormalization, first-order transitions and demagnetizing effects for Schofield's linear model

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

doi:10.1016/0378-4371(81)90063-7

Cited by 8 publications

(4 citation statements)

References 12 publications

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“…The result agrees well with our proposed formula. In the present paper, we studied only the case of ferromagnetic long-range interactions, but we note in passing that with J 0 < 0, (5) may serve as a useful approximation for static 31 and dynamic 32 demagnetizing effects. We further note that our model can be considered a well-stirred approximation for the Ising model on a small-world network.…”

Section: Discussionmentioning

confidence: 99%

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: Discussionmentioning

confidence: 99%

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

et al. 2011

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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%

“…In 1968, Fisher produced a general theory for critical systems under constraint and the general process linking the ideal critical exponents to those for the constrained system became known as Fisher renormalisation [4]. 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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“…Extensive reviews of the topic are given in [1,2], which, besides the general theory, also contain discussions of experimental relevance and results. One aspect that appears to be neglected in the literature is amplitude ratios in thermodynamic systems subject to constraint, a topic of importance for real systems [3][4][5]. The effects of such constraints on the critical exponents of experimental measurements are well known and well understood; the exponents may differ significantly from their ideal, or pure, theoretical counterparts.…”

Section: Introductionmentioning

confidence: 99%

Universal amplitude ratios for constrained critical systems

Измаилян¹,

Kenna²

2014

J. Stat. Mech.

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The critical properties of systems under constraint differ from their ideal counterparts through Fisher renormalization. The mathematical properties of Fisher renormalization applied to critical exponents are well known: the renormalized indices obey the same scaling relations as the ideal ones and the transformations are involutions in the sense that re-renormalizing the critical exponents of the constrained system delivers their original, ideal counterparts. Here we examine Fisher renormalization of critical amplitudes and show that, unlike for critical exponents, the associated transformations are not involutions. However, for ratios and combinations of amplitudes which are universal, Fisher renormalization is involutory.

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Critical-exponent renormalization, first-order transitions and demagnetizing effects for Schofield's linear model

Cited by 8 publications

References 12 publications

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

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

Critical phenomena for systems under constraint

Universal amplitude ratios for constrained critical systems

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