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

##### Physics Department and Institute for Advanced Scientific Computation, Extremadura University, Spain

Spin glasses are the paradigm of complex systems. The canonical one is
a diluted alloy with a metal base (e.g. copper) with magnetic
(diluted) impurities (e.g. manganese). These materials present a
really slow dynamics. However, the nature of the spin glass phase in
finite dimensional systems is still controversial.

In this lecture different theories which describe the low temperature
phase will be discussed: droplet, replica symmetry breaking and
chaotic pairs

[1,2,3]
In particular we will use in this lecture the framework of Field
Theory, discussing critical exponents at and below the phase
transition, existence of a phase transition in a magnetic field, the
computation of the lower critical dimension (in presence/absence of an
external magnetic field)

[2], and finally we will introduce some
rigorous 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 the
correlation functions in the spin glass phase

[5], the computation of
the probability distribution of the overlap (the order parameter) by
means 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.