Existence of a phasetransition in a onedimensional Ising ferromagnet
Abstract
Existence of a phasetransition is proved for an infinite linear chain of spins μ_{ j }=±1, with an interaction energy 220_2005_Article_BF01645907_TeX2GIFE1.gif H =  sum J(i  j)μ _i μ _j , where J( n) is positive and monotone decreasing, and the sums Σ J( n) and Σ (log log n) [ n ^{3} J( n)]^{1} both converge. In particular, as conjectured by Kac and Thompson, a transition exists for J( n)= n ^{α} when 1 < α < 2. A possible extension of these results to Heisenberg ferromagnets is discussed.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 June 1969
 DOI:
 10.1007/BF01645907
 Bibcode:
 1969CMaPh..12...91D