Study of stiffness energy on fractals

CORNETTE V.; RAMIREZ PASTOR A. J.; NIETO F.

San Rafael- Mendoza

Taller; TREFEMAC 2007; 2007

UTN Facultad Regional San Rafael- UNSL

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 di®erent 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 µ plays a central role in the droplet picture. It is usually calculated by using the concept of defect energy, ∆F = Fa - Fp, which is the diference 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, ∆F ~ Lθ, with θ = 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 µ (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.