Juan J. Ruiz-Lorenzo photo

NATURE OF THE SPIN GLASS PHASE IN FINITE DIMENSIONAL (ISING) SPIN GLASSES

Juan J. Ruiz-Lorenzo (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 Aizenman-Wehr 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 out-of-equilibrium numerical simulations[7] and the existence of a phase transition in an external field [8].

References:

[1] T. Castellani and A. Cavagna. Spin-Glass Theory for Pedestrians. Stat. Mech. (2005) P05012 . arXiv:cond-mat/0505032 .
[2] C. De Dominicis and I. Giardina. Random Fields and Spin Glasses: A Field Theory Approach. Cambridge University Press, 2010.
[3] N. Read. Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking. Phys. Rev. E 90, 032142 (2014). arXiv:1407.4136.
[4] A. Billoire, et al. Numerical construction of the Aizenman-Wehr metastate. Phys. Rev. Lett. 119, 037203 (2017). arXiv:1704.01390.
[5] R. Alvarez Banos et al. Nature of the spin-glass phase at experimental length scales. J. Stat. Mech (2010) P06026. arXiv:1003.2569.
[6] D. Herisson and M. Ocio, Fluctuation-dissipation ratio of a spin glass in the aging regime. Phys. Rev. Lett. 88, 257202 (2002). arXiv:cond-mat/0112378.
[7] M. Baity-Jesi et al. A statics-dynamics equivalence through the fluctuation dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements. Proceedings of the National Academy of Sciences of USA (PNAS) 114 (8) 1838-1843 (2017). arXiv:1610.01418.
[8] R. Alvarez Banos et al. Thermodynamic glass transition in a spin glass without time-reversal symmetry. Proceedings of the National Academy of Sciences of USA (PNAS) 109 (17) 6452 (2012). arXiv:1202.5593.