On the critical thermodynamics of inhomogeneous systems

Abstract

Wilson's renormalization group approach, in the original wave packet approximation, is used to discuss the critical properties of inhomogeneous systems within the paramagnetic region, starting with a position-dependent n-component classical hamiltonian corresponding to Ising, XY, and Heisenberg spin systems, respectively. Both spatially periodic and aperiodic inhomogeneities are considered. The possibilities of local or global critical behaviour are discussed. For periodically inhomogeneous systems, the critical behaviour is the same as for homogeneous systems. For aperiodically inhomogeneous systems with n < 4, a new “random” fixed point is obtained with a specific heat exponent α = 0. Finally, stable quasi homogeneous critical behaviour is possible for n 4, where α < 0. For n = 4, the critical exponents depend continuously on the disorder.