publication . Article . Other literature type . 1969

Non-existence of spontaneous magnetization in a one-dimensional Ising ferromagnet

Dyson, Freeman J.;
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  • Published: 01 Sep 1969 Journal: Communications in Mathematical Physics, volume 12, pages 212-215 (issn: 0010-3616, eissn: 1432-0916, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
It is proved that an infinite linear chain of spins μj=±1, with an interaction energy $$H = - \Sigma J(i - j)\mu _i \mu _j $$ has zero spontaneous magnetization at all finite temperatures, provided thatJ (n) is non-negative and that $$H = - \Sigma J(i - j)\mu _i \mu _j $$ . This shows that a theorem ofRuelle, establishing the absence of long-range order when the sum Σn J (n) converges, is not the best possible.
Subjects
free text keywords: Mathematical Physics, Statistical and Nonlinear Physics, Mathematical analysis, Ferromagnetism, Ising model, Spontaneous magnetization, Physics, Interaction energy, Spins, Condensed matter physics, Sigma
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publication . Article . Other literature type . 1969

Non-existence of spontaneous magnetization in a one-dimensional Ising ferromagnet

Dyson, Freeman J.;