About: Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces

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About: Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We consider continuous-spin models on the d-dimensional hypercubic lattice with the spins sigma(x) a priori uniformly distributed over the unit sphere in R^n and the interaction energy having two parts: a short-range part, represented by a potential Phi, and a long-range antiferromagnetic part lambda \|x-y\|^(-s) sigma (x) dot sigma (y) for some exponent s } d and lambda}0. We assume that Phi is twice continuously differentiable, finite range and invariant under rigid rotations of all spins. For s in the interval (d,d+2] and any lambda } 0, we then show that the expectation of each sigma (x) vanishes in all translation-invariant Gibbs states. In particular, the spontaneous magnetization is zero and block-spin averages vanish in all (translation invariant or not) Gibbs states. This contrasts the situation of lambda=0 where the ferromagnetic nearest-neighbor systems in d}2 exhibit strong magnetic order at sufficiently low temperatures. Our theorem extends an earlier result of A. van Enter ruling out magnetized states with uniformly positive two-point correlation functions. We consider continuous-spin models on the d-dimensional hypercubic lattice with the spins sigma(x) a priori uniformly distributed over the unit sphere in R^n and the interaction energy having two parts: a short-range part, represented by a potential Phi, and a long-range antiferromagnetic part lambda \|x-y\|^(-s) sigma (x) dot sigma (y) for some exponent s } d and lambda}0. We assume that Phi is twice continuously differentiable, finite range and invariant under rigid rotations of all spins. For s in the interval (d,d+2] and any lambda } 0, we then show that the expectation of each sigma (x) vanishes in all translation-invariant Gibbs states. In particular, the spontaneous magnetization is zero and block-spin averages vanish in all (translation invariant or not) Gibbs states. This contrasts the situation of lambda=0 where the ferromagnetic nearest-neighbor systems in d}2 exhibit strong magnetic order at sufficiently low temperatures. Our theorem extends an earlier result of A. van Enter ruling out magnetized states with uniformly positive two-point correlation functions. (en)
Title	Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces (en)
skos:prefLabel	Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces (en)
skos:notation	RIV/60076658:12510/11:43871381!RIV12-MSM-12510___
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Biskup, Marek
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Jihočeská univerzita v Českých Budějovicích / Ekonomická fakulta
http://linked.open...dnocenehoVysledku	184316
http://linked.open...ai/riv/idVysledku	RIV/60076658:12510/11:43871381
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Modulated phase; Long-range forces; Antiferromagnetic interaction; Magnetic order (en)
http://linked.open.../riv/klicoveSlovo	Antiferromagnetic interaction Long-range forces Magnetic order Modulated phase
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[AB46E064093E]
http://linked.open...i/riv/nazevZdroje	Journal of Statistical Physics
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	144
http://linked.open...iv/tvurceVysledku	Biskup, Marek Crawford, Nicholas
http://linked.open...ain/vavai/riv/wos	000294228400001
issn	0022-4715
number of pages	18 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s10955-011-0274-z
http://localhost/t...ganizacniJednotka	12510

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