Effective long range order and phase transitions in finite, macroscopic one and two dimensional systems

Imry, Y.

doi:10.1016/0003-4916(69)90345-5

Cited by 52 publications

(11 citation statements)

References 17 publications

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“…For finite (but still large) systems discontinuities of thermodynamic quantities and infinite range correlations are not necessary. "Discontinuities" have finite widths and correlation ranges may be as large as the system itself, regardless of the behaviour in the thermodynamic limit 18 . What is more finite systems can show interesting effects which will be wiped away in the thermodynamic limit.…”

Section: Discussionmentioning

confidence: 99%

“…where (18) was the basis of our previous investigations 2 of spontaneous self-sustaining currents (see Eq. ( 50), (51)).…”

Section: Mean Field Approximation Of Magnetostatic Couplingmentioning

confidence: 99%

“…( 50), (51)). Its derivation from the long-range current-current interaction serves as a justification of the use of the Hamiltonian (18) to investigate magnetic properties of mesoscopic systems.…”

Section: Mean Field Approximation Of Magnetostatic Couplingmentioning

confidence: 99%

“…It is true for systems in the thermodynamic limit with short-range interactions. However, one can look for the conditions for an ordered state for large but finite number of interacting entities 18 .…”

Section: Flux Trapped In Mesoscopic Cylindersmentioning

confidence: 99%

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Possibility of long-range order in clean mesoscopic cylinders

Lisowski

Zipper²,

Stebelski³

1999

Phys. Rev. B

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A microscopic Hamiltonian of the magnetostatic interaction is discussed. This long-range interaction can play an important role in mesoscopic systems leading to an ordered ground state. The self-consistent mean field approximation of the magnetostatic interaction is performed to give an effective Hamiltonian from which the spontaneous, self-sustaining currents can be obtained. To go beyond the mean field approximation the mean square fluctuation of the total momentum is calculated and its influence on self-sustaining currents in mesoscopic cylinders with quasi-1D and quasi-2D conduction is considered. Then, by the use of the microscopic Hamiltonian of the magnetostatic interaction for a set of stacked rings, the problem of long-range order is discussed. The temperature $T^{*}$ below which the system is in an ordered state is determined.Comment: 14 pages, REVTeX, 5 figures, in print in Phys. Rev.

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Section: Discussionmentioning

confidence: 99%

“…where (18) was the basis of our previous investigations 2 of spontaneous self-sustaining currents (see Eq. ( 50), (51)).…”

Section: Mean Field Approximation Of Magnetostatic Couplingmentioning

confidence: 99%

Section: Mean Field Approximation Of Magnetostatic Couplingmentioning

confidence: 99%

Section: Flux Trapped In Mesoscopic Cylindersmentioning

confidence: 99%

See 2 more Smart Citations

Possibility of long-range order in clean mesoscopic cylinders

Lisowski

Zipper²,

Stebelski³

1999

Phys. Rev. B

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“…The authors also stressed, that the impossibility of spontaneous magnetisation does not exclude the existence of other types of phase transitions in these models. For the theorem to apply, it is important that long-range interactions are sufficiently suppresssed [3,4]. In 1967 Wegner [5] confirmed this for the ferromagnetic Heisenberg model with reduced O(2)symmetry (∼XY-model), by showing, based on a low-temperature expansion, that the spin-spin correlation function in one and two dimensions always converges to zero at sufficiently large distances.…”

Section: Introductionmentioning

confidence: 94%

Infinite-range correlations in 1D systems with continuous symmetry

Rindlisbacher¹

2020

Preprint

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O(N )-symmetric lattice scalar fields are considered, coupled to a chemical potential and source terms. At the example of N = 2, it is shown that such systems can even in (0+1) dimensions produce infinite-range correlations and a non-zero vacuum expectation value whenever the chemical potential assumes certain discrete values. Different mechanisms for how the latter phenomena are produced are discussed, depending on whether source terms are set to zero or non-zero values. In the conclusion, the relation of these findings to the Mermin-Wagner theorem is addressed.

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High temperature superconductivity

Ginzburg

1970

J. polym. sci., C Polym. symp.

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The critical temperature, Tc, for all presently known superconductors does not exceed 21'K. This fact obviously limits the range of applications of superconductivity in technology in a very fundamental way. On the whole, the reason why the value of Tc for “ordinary” superconductors would not exceed 20‐40oK is fairly well understood. At the same time, there apparently could exist high temperature superconductors for which Tc would reach liquid air temperature or even room temperatures. Possible means of producing high temperature superconductors are considered in this article which is based on the review published in Contemporary Physics, 9, 355 (1968), but includes also some new material. Special attention is paid to what can be called the exciton mechanism of superconductivity and its application to systems of the “sandwich” type and metallic conductors with layer structures.

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Effective long range order and phase transitions in finite, macroscopic one and two dimensional systems

Cited by 52 publications

References 17 publications

Possibility of long-range order in clean mesoscopic cylinders

Possibility of long-range order in clean mesoscopic cylinders

Infinite-range correlations in 1D systems with continuous symmetry

High temperature superconductivity

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