Criticality of the discrete N-vector ferromagnet in a cubic lattice with a free surface

Abstract

We study a discrete N-component spin ferromagnet with Hamiltonian β H= −NK ∑ 〈i,j〉 ( S i· S j)−N 2L ∑ 〈i,j〉 ( S i· S j) 2 in a semi-infinite cubic lattice. The coupling constants at the surface, K s and L s, are allowed to be different from the bulk ones, K B and L B. Using a simple real-space renormalization group procedure we obtain the N-evolution ( N real) of the phase diagram, including the N→0 and N→∞ limits. The thermal ( v) and crossover (φ) critical exponents at various critical and multicritical points are calculated.