Consider the ising ferromagnet, given by the spin hamiltonian h--jσσσ; - η σσ,. (ij) i-1 where j> 0, ai= t1 , and the first sum is over nearest neighbors on a simple triangular lattice. use the real-space renormalization-group scheme of niemeyer and van leeuwen, up to first-order terms, as dis- cussed in the last section, to obtain the thermal and magnetic critical exponents. consider the ising ferromagnet, given by the hamiltonian n m= -jσσ.σ; -η σσ, i=1 (ij) where j> 0, oi = ±1, and the first sum is over nearest-neighbor sites on a square lattice. choose a unit cell consisting of five spins, as indicated in figure 14.9. use the real-space renormalization-group scheme of niemeyer and van leeuwen to write a set of recursion relations up to first-order terms in the interactions. obtain the values of the thermal and magnetic critical exponents.