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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F11%3A43871381" target="_blank" >RIV/60076658:12510/11:43871381 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10955-011-0274-z" target="_blank" >http://dx.doi.org/10.1007/s10955-011-0274-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10955-011-0274-z" target="_blank" >10.1007/s10955-011-0274-z</a>

Result language
angličtina
Original language name
Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces
Original language 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 theinterval (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 invariantor 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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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