Study of stiffness energy on fractals

CORNETTE V.; NIETO F.; RAMÍREZ-PASTOR A. J.

Los Reyunos, San Rafael, Mendoza, Argentina

Taller; V Taller Regional de Física Estadística y sus Aplicaciones a la Física de la Materia Condensada (TREFEMAC); 2007

The present work focuses on the order-disorder transition of an Ising model on fractals surface. We present a detailed numerical study, based on the Monte Carlo method by analyzing the domain-wall energy, of the critical temperature of the Ising model on some two-dimensional deterministic and non-deterministic fractal lattices with different Hausdorff dimensions. Those with finite ramification order do not display ordered phases at any finite temperature, whereas the lattices with infinite connectivity show genuine critical behavior. The exponent q plays a central role in the droplet picture. It is usually calculated by using the concept of defect energy, DF = Fa− Fp, which is the difference between the ground-state (GS) energies for antiperiodic (Fa) and periodic (Fp) boundary conditions, in one of the directions of a d-dimensional system of linear size L. In ferromagnetic systems, DF ~ Lq, with q= ds = d−1, because the induced defect is a (d-1 )-dimensional domain-wall with all their bonds frustrated. A positive value of the stiffness exponent q (T=0 ) indicates the existence of a phase transition for non-zero temperature. The data show in a clear way the existence of an order-disorder transition at finite temperature in this systems.