Critical exponents for two-dimensional Heisenberg ferromagnet with long-range interaction

Abstract

Using renormalization group technique, the critical exponents are determined for two-dimensional Heisenberg ferromagnet in the presence of a magnetic field. Critical exponents are expressed as a function of potential range σ. For the long-range interaction potential between the spins, the spontaneous magnetization exponent β takes the poorer value of mean-field result. The other exponents agree with the known values of exponents. The susceptibility eigenvalue equation arising from renormalization group is also solved and eigenfunctions are determined.