Surface and corner magnetizations in the two-dimensional Ising model

Michael N. Barber, Ingo Peschel, Paul A. Pearce

Michel Pleimling, Walter Selke

Using Monte Carlo techniques, Ising cubes with ferromagnetic nearest-neighbor interactions and enhanced couplings between surface spins are studied. In particular, at the surface transition, the corner magnetization shows nonuniversal, coupling-dependent critical behavior in the thermodynamic limit. Results on the critical exponent of the corner magnetization are compared to previous findings on two-dimensional Ising models with three intersecting defect lines.

Yu. M. Zinoviev

István A. Kovács, Ferenc Iglói

Using the strong disorder renormalization group method, we study numerically the critical behavior of the random transverse Ising model at a free surface, at a corner, and at an edge in two-, three-, and four-dimensional lattices. The surface magnetization exponents are found to be ${x}_{s}=1.60(2),$ 2.65(15), and $3.7(1)$ in $D=2,$ 3, and 4, respectively, which do not depend on the form of disorder. We have also studied critical magnetization profiles in slab, pyramid, and wedge geometries with fixed-free boundary conditions and analyzed their scaling behavior.

Douglas B. Abraham, F. T. Latrémolière

We obtain exact results at all temperatures for the two-point function of surface spins near the corner of a two-dimensional rectangular Ising ferromagnet; at the critical point, the functional form predicted by conformal theory is recovered. We are also able to calculate exactly a large class of correlation functions involving spins off the surface, and to interpret the results geometrically.

R. Z. Bariev, O.A. Malov, N.A. Barieva