New insight into the thermodynamics of Heisenberg ferromagnets as inferred from high-temperature series

Abstract In search of a suitable equation of state for ferromagnets, we revise the information about the Heisenberg model obtainable from high-temperature series. Special attention is paid to the ratio χ 3 / χ 4 (where χ ⁢ a n d ⁢ χ 3 are the linear and cubic susceptibilities) related to Landau's quartic coefficient b . It is found in particular that both χ 3 / χ 4 and b tend to a finite limit as T → T C . This limit is small — an order of magnitude smaller than predicted by Weiss's molecular field and similar theories — but contrary to the common belief, nonzero. This implies a rejection of the generally accepted critical-point exponents and a return to those of Landau: α = 0 , β = 1 2 , γ = 1 , etc.