Low-temperature renormalization group for ferromagnets with long-range interactions

Ferromagnets with the number of spin components $n>2$ and with power-law interactions r^-d-σ are studied in dimensions d=2+ε for small ε. The following theorem is proved: Let ηSR be the value of the critical exponent η for short-range force (e.g., nearest-neighbor exchange). Then in the presence of the long-range power-law interaction the critical behavior is the same as for short-range interactions provided that the inequality 2-σ<ηSR is satisfied. In this case the critical exponents depend on d and n but not on σ. In the opposite case, the value of η is ηLR=2-σ and the critical exponent ν depends on σ in addition to d and n.