Absence of spontaneous magnetization in isotropic partially finite systems

Costache, G.; Nenciu, G.

doi:10.1016/0375-9601(70)90728-0

Cited by 7 publications

(2 citation statements)

References 5 publications

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“…Costache and Nenciu [38] discuss the overall magnetization of a partially finite three-dimensional Heisenberg model and reproduce the generalization expected from the arguments by Chester et al A similar, though much more exhaustive, discussion has been given by Fisher and Jasnow in two papers [39], [40], where the authors discuss Bose systems with respect to off-diagonal ordering, and spin systems with respect to a magnetic phase transition. The general procedure is to embed the space Ω occupied by the physical system into an enclosing "box" Λ and, furthermore, to allow for a decomposition of Ω into "subdomains" Γ.…”

Section: Partially Restricted Systemsmentioning

confidence: 59%

The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

Gelfert¹,

Nolting²

2001

J. Phys.: Condens. Matter

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After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the Periodic Anderson Model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in manybody physics is discussed on a conceptual level.

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Section: Partially Restricted Systemsmentioning

confidence: 59%

The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

Gelfert¹,

Nolting²

2001

J. Phys.: Condens. Matter

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“…It has been shown by Costache and Nenciu (5) that the statement of Mermin and Wagner retains its validity also for systems of restricted dimensionality in which one o r two dimensions go to infinity whereas the others a r e kept fixed. Ritchie and Fisher (6) have proved that despite of vanishing of the magnetization, the static susceptibility of thin films for isotropic Heisenberg Hamiltonian diverges at a f inite temperature.…”

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confidence: 94%

Stanley‐Kaplan Phase Transition in Two‐Layered Heisenberg Spin Systems

Zagórski

Sukiennicki

1974

Physica Status Solidi (b)

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The restricted-dimensional magnets have became recently a subject of numerov theoretical studies. Mermin and Wagner (1) have proved rigorously the absence of a spontaneous magnetization in the isotropic two-dimensional Heisenberg model at any finite temperature. On the other hand, Stanley and Kaplan (2) have shown that the static zero-field susceptibility diverges at a finite temperature. Their result , obtained by means of the high temperature series expansion, suggests the existence of a phase transition in two-dimensional ferromagnets. Some insight into the mechanism of such a phase transition was given by Mubayi and Lange (3) and Oguchi (4). It has been shown by Costache and Nenciu (5) that the statement of Mermin andWagner retains its validity also for systems of restricted dimensionality in which one o r two dimensions go to infinity whereas the others a r e kept fixed. Ritchie and Fisher (6) have proved that despite of vanishing of the magnetization, the static susceptibility of thin films for isotropic Heisenberg Hamiltonian diverges at a f inite temperature. However, the method used by them does not work for systems with spin S = 1/2.The purpose of this note is to examine the possibility of the Stanley-Kaplan-like phase transition for two-layered Heisenberg spin systems with S = 1/2 using the method outlined by Mubayi and Lange. Such a system can be treated a s an ultra-thin film consisting of only two planes, constituting -for simplicity -simple cubic structure with (100) orientation of its surfaces. In this case the Green functions G.. = = (

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Molecular Field Theory and Phase Transitions in Partially Finite Spin Systems

Angelescu

Costache

Nenciu

1972

Physica Status Solidi (b)

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A molecular field model of an homogeneous thin film with free surfaces is studied. The existence of one and only one phase transition, which is of second order, is proved. A study is made of the distribution of magnetization across the film thickness. I n the limit of infinite number of layers, a description of the bulk is obtained, which is equivalent to the Weiss molecular field description. The critical temperature of the film approaches the bulk critical temperature as the inverse square of the number of layers.On Btudie un modhle de champ moleculaire pour une couche mince homogene it surfaces libres. On prouve qu'il existe une transition de phase et seulement une, et qu'elle est d u second ordre. De meme, on Btudie la distribution de la magnetisation A l'intbrieur de la couche. Quand le nombre de plans de la couche tend vers l'infini, on obtient une description du massiff Bquivalente it la theorie de Weiss. La difference des temperatures critiques de la couche e t d u massiff tend vers zero comme I'inverse du carrB du nombre de plans.

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Absence of spontaneous magnetization in isotropic partially finite systems

Cited by 7 publications

References 5 publications

The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

Stanley‐Kaplan Phase Transition in Two‐Layered Heisenberg Spin Systems

Molecular Field Theory and Phase Transitions in Partially Finite Spin Systems

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