caa a22 4500 445391286 CHVBK 20180317143047.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s10955-011-0274-z doi (NATIONALLICENCE)springer-10.1007/s10955-011-0274-z Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces [Elektronische Daten] [Marek Biskup, Nicholas Crawford] We consider continuous-spin models on the d-dimensional hypercubic lattice with the spinsσ x a priori uniformly distributed over the unit sphere inℝ n (withn≥2) and the interaction energy having two parts: a short-range part, represented by a potentialΦ, and a long-range antiferromagnetic part λ|x−y|−s σ x ⋅σ y for some exponents>d and λ≥0. We assume thatΦ is twice continuously differentiable, finite range and invariant under rigid rotations of all spins. For d≥1,s∈(d,d+2] and any λ>0, we then show that the expectation of eachσ 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 ofλ=0 where the ferromagnetic nearest-neighbor systems ind≥3 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. Springer Science+Business Media, LLC, 2011 Magnetic order nationallicence Antiferromagnetic interaction nationallicence Long-range forces nationallicence Modulated phase nationallicence Biskup Marek Department of Mathematics, UCLA, Los Angeles, CA, USA aut Crawford Nicholas Department of Industrial Engineering, Technion, Haifa, Israel aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/4(2011-08-01), 731-748 0022-4715 144:4<731 2011 144 10955 https://doi.org/10.1007/s10955-011-0274-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0274-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Biskup Marek Department of Mathematics, UCLA, Los Angeles, CA, USA aut NATIONALLICENCE 700 1- Crawford Nicholas Department of Industrial Engineering, Technion, Haifa, Israel aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/4(2011-08-01), 731-748 0022-4715 144:4<731 2011 144 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer