Inhomogeneous ground state and the coexistence of two length scales near phase transitions in real solids

Real crystals almost unavoidably contain a finite density of dislocations. We show that this generic type of long--range correlated disorder leads to a breakdown of the conventional scenario of critical behavior and standard renormalization group techniques based on the existence of a simple, homogeneous ground state. This breakdown is due to the appearance of an inhomogeneous ground state that changes the character of the phase transition to that of a percolative phenomenon. This scenario leads to a natural explanation for the appearance of two length scales in recent high resolution small-angle scattering experiments near magnetic and structural phase transitions.Comment: 4 pages, RevTex, no figures; also available from http://www.tp3.ruhr-uni-bochum.de/archive/tpiii_archive.htm

Critical behavior of Ising models with static site dilution

A Monte Carlo analysis of the ferromagnetic spin-1/2 Ising model with nearest-neighbor interactions and static (quenched) site dilution, where a fraction x, 0≤x≤0.2, of the spins in a simple-cubic lattice are randomly replaced by vacant sites, reveals effective critical exponents varying continuously with x