Critical and Multicritical Points, Lines and Surfaces of Spin Glasses in the Presence of Magnetic Fields and Anisotropy

Abstract

As Dr. Young has pointed out in his lectures¹ the mean field theory of a simple model Ising spin glass² is much more subtle than that of a conventional magnet while normal renormalization group theory applied to short-ranged models³ yields perplexing and apparently unphysical ^4,5 results, even in the paramagnetic phase. I shall not attempt here to improve upon the RG problem but rather to develop further the parameter space of potentially interesting mean field problems in the hope of demonstrating a great richness of phases, transitions and crossovers. Thus, I shall restrict my comments to infinite-ranged models studied within replica theory⁶ but with the full panoply of replica-symmetry (RS) breaking⁷.