Heisenberg Spin Glasses: Large Lattices at Low Temperatures

Abstract

Spin-glasses are disordered magnetic alloys with very unusual behaviour. Interest in spin glasses goes far beyond just this class of materials, however, because they provide a convenient model system from which to derive a unified theory of the glassy state (glass is one of the most common, yet mysterious states of condensed matter). Interest in spin glasses also extends outside of condensed matter physics because there has been a fruitful exchange of ideas between the spin glass community and researchers in other branches of science such as computer scientists working on combinatorical optimization. Simple analytical approximations predict that spin glasses have a finite temperature transition, but whether this actually occurs (or is an artefact of the approximations used) has remained unclear, at least for a variety known as “Heisenberg spin glasses”. The advent of a new generation of simulation algorithms, finite-size scaling analysis and parallel computers have mean that, at last, we can make a serious attempt to fully understand the phase transition in Heisenberg spin glasses.