Real-space renormalization-group transformation for finite thickness ising systems

Abstract

The real-space renormalization group transformation based on the cumulant expansion is modified for systems with free-surface boundary conditions. Free energies and heat capacities of ferromagnetic strips (n x ∞) and slabs (n x ∞ x ∞) are determined over a wide temperature range. The critical or pseudocritical behavior approaches the bulk limit as n → ∞ according to a simple power law, [T c(n) − T c (∞)] ∞n −λ it is verified that the shift exponent λ is equal to the reciprocal of the critical length exponent.