Stiffness exponent, number of pure states, and Almeida-Thouless line in spin-glasses

Abstract

We show how an inequality for the stiffness exponent for spin-glass models proposed by Fisher and Huse could be violated. We analyze their derivation and point out that their scaling arguments do not apply to investigations of the difference between systems with periodic and antiperiodic boundary conditions. As a consequence, the possibility remains open that in sufficiently high dimensions an infinite number of pure states exists and that an Almeida-Thouless line-spin-glass transition in a field-occurs, as is predicted in competing theories.