Ferromagnetism, antiferromagnetism, and the curious nematic phase ofS=1quantum spin systems

Abstract

Original citation: Ueltschi, Daniel. (2015) Ferromagnetism, antiferromagnetism, and the curious nematic phase ofS=1 quantum spin systems. Physical Review E, 91 (4). 042132. Permanent WRAP URL:http://wrap.warwick.ac.uk/80071 Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher statement: © 2015 American Physical Society A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP URL' above for details on accessing the published version and note that access may require a subscription. Ferromagnetism, antiferromagnetism, and the curious nematic phase of S = 1 quantum spin systems Daniel UeltschiDepartment of Mathematics, University of Warwick, Coventry, CV4 7AL, United Kingdom *We investigate the phase diagram of S = 1 quantum spin systems with SU(2)-invariant interactions, at low temperatures and in three spatial dimensions. Symmetry breaking and the nature of extremal states can be studied using random loop representations. The latter confirm the occurrence of ferro-and antiferromagnetic transitions and the breaking of SU(3) invariance. And they reveal the peculiar nature of the nematic extremal states which minimize x (S i x ) 2 .

Universal Behaviour of 3D Loop Soup Models

“…The minus signs in the matrix elements of P xy cancel when S ∈ N, but the representation for half-integer spins has unwelcome signs. See [38] for more details.…”

“…But not too many useful consequences have so far been unearthed. We discuss here quantum spin systems and the symmetry of the low-temperature phases, following [38].…”

Existence of Néel Order in the S=1 Bilinear-Biquadratic Heisenberg Model via Random Loops

“…In Section 5 the connection between the loop model and the quantum system is proved. In particular it is shown how to write various correlation functions in terms of probabilities of events in the loop model; some of these correlations are also presented in [22]. In Section 6 the main result concerning Néel order is presented and proved.…”

Сверхтвердая Магнитная Фаза В Двумерном Изингоподобном Антиферромагнетике С Большой Одноионной Анизотропией

“…Таким образом, можно утверждать, что приближение среднего поля можно использовать при рассмотрении данной модели. Кроме того, как было доказано в [26,27], приближение среднего поля можно использовать при рассмотрении систем лю-бой размерности. Также необходимо отметить работу [5], где было показано, что приближение среднего поля дает правильные результаты для модели Гейзенберга с фрустрированным обменным взаимодействием для спина 1/2, в частности при исследовании сверхтвердой магнитной фазы.…”

“…В таких магнетиках квантовые свойства отдельных спинов в эффективном магнитном поле играют решающую роль в формировании динамических и термодинамических свойств [26,27]. Влияние большой одноионной анизотро-пии проявляется, в том числе, в квантовом сокраще-нии спина, приводящем к тому, что среднее значение намагниченности (векторный параметр порядка) на узле равно нулю, и в системе реализуется дальний магнитный порядок тензорного типа -квадрупольная фаза.…”