Renormalization group free energy for an ising ferromagnet on a simple cubic lattice

W. Reich, H. Cofta

H. O. M�rtin, Constantino Tsallis

M. Fähnle, T. Holey, U. Staaden +1 more

L. R. da Silva, Constantino Tsallis, Enaldo F. Sarmento

We study the phase diagram and universality classes of the quenched bond-diluted spin-(1/2 Ising ferromagnet in a semi-infinite simple-cubic lattice with a (001) free surface. The approach (herein formulated for arbitrary values of the number of states q of the Potts model) is a real-space renormalization group which preserves two-spin correlation functions and uses clusters which have already proved to be very appropriate for the present structure. We observe that surface ferromagnetism persists below the two-dimensional (2D) percolation threshold ${p}_{c}^{2\mathrm{D}=(1/2}$, in fact down to ${p}_{c}$\ensuremath{\simeq}0.42. In addition to that we check that a conjectural extension of the Kasteleyn-Fortuin theorem is satisfied in the present particular case.

Michael Nauenberg

Lawrence G. Dunfield, Jaan Noolandi

We use a real-space renormalization transformation with a cumulant expansion, modified to include free-surface boundary conditions, to study the critical behavior of semi-infinite ferromagnetic systems. We present first-order calculations for the Ising model on the semi-infinite square and simple cubic lattices. Our results serve as the basis of a critical discussion of previous real-space and momentum-space renormalization-group calculations.