
NATURE OF THE SPIN GLASS PHASE IN FINITE DIMENSIONAL (ISING) SPIN GLASSESJuan J. RuizLorenzo (Personal webpage)Physics Department and Institute for Advanced Scientific Computation, Extremadura University, Spain
Spin glasses are the paradigm of complex systems. The canonical one isa diluted alloy with a metal base (e.g. copper) with magnetic(diluted) impurities (e.g. manganese). These materials present areally slow dynamics. However, the nature of the spin glass phase infinite dimensional systems is still controversial. In this lecture different theories which describe the low temperaturephase will be discussed: droplet, replica symmetry breaking andchaotic pairs [1,2,3]. In particular we will use in this lecture the framework of FieldTheory, discussing critical exponents at and below the phasetransition, existence of a phase transition in a magnetic field, thecomputation of the lower critical dimension (in presence/absence of anexternal magnetic field) [2], and finally we will introduce somerigorous results based in the concept of metastate [3]. Lastly, we will present some numerical results regarding the construction of the AizenmanWehr metastate [4], the scaling of thecorrelation functions in the spin glass phase [5], the computation ofthe probability distribution of the overlap (the order parameter) bymeans of experiments [6] and outofequilibrium numerical simulations[7] and the existence of a phase transition in an external field [8].
References:
[1] T. Castellani and A. Cavagna. SpinGlass Theory for Pedestrians. Stat. Mech. (2005) P05012 . arXiv:condmat/0505032 . 