We characterize the phase diagram of anisotropic Heisenberg spin glasses, finding both the spin and the chiral glass transition. We remark on the presence of strong finite-size effects in the chiral sector. On the spin glass sector, we find that the universality class is that of Ising spin glasses. Our data are compatible with a unique phase transition for the chiral and spin glass sector. We focus on keeping finite-size effects under control, and we stress that they are important to understand experiments. Thanks to large GPU clusters we have been able to thermalize cubic lattices with up to ${64}^{3}$ spins, over a vast range of temperatures (hence, of relaxation times).We characterize the phase diagram of anisotropic Heisenberg spin glasses, finding both the spin and the chiral glass transition. We remark on the presence of strong finite-size effects in the chiral sector. On the spin glass sector, we find that the universality class is that of Ising spin glasses. Our data are compatible with a unique phase transition for the chiral and spin glass sector. We focus on keeping finite-size effects under control, and we stress that they are important to understand experiments. Thanks to large GPU clusters we have been able to thermalize cubic lattices with up to ${64}^{3}$ spins, over a vast range of temperatures (hence, of relaxation times).

arXiv:1309.1599Physical Review BJan 21, 201432 citations

Nature of the Spin Glass Phase in Finite Dimensional (Ising) Spin Glasses

Juan Jesus Ruiz-Lorenzo

Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low temperature phase have been proposed: droplet, replica symmetry breaking and chaotic pairs. We present analytical studies of critical properties of spin glasses, in particular, critical exponents at and below the phase transition, existence of a phase transition in a magnetic field, computation of the lower critical dimension (in presence/absence of a magnetic field). We also introduce some rigorous results based on the concept of metastate. Finally, we report some numerical results regarding the construction of the Aizenman-Wehr metastate, scaling of the correlation functions in the spin glass phase and existence of a phase transition in a field, confronting these results with the predictions of different theories.Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low temperature phase have been proposed: droplet, replica symmetry breaking and chaotic pairs. We present analytical studies of critical properties of spin glasses, in particular, critical exponents at and below the phase transition, existence of a phase transition in a magnetic field, computation of the lower critical dimension (in presence/absence of a magnetic field). We also introduce some rigorous results based on the concept of metastate. Finally, we report some numerical results regarding the construction of the Aizenman-Wehr metastate, scaling of the correlation functions in the spin glass phase and existence of a phase transition in a field, confronting these results with the predictions of different theories.

arXiv:2006.12930WORLD SCIENTIFIC eBooksJun 24, 20201 citation

{64}^{3}

spins, over a vast range of temperatures (hence, of relaxation times).