Dottorato in FISICA

Titolo della tesi: From glassy bulk systems to spin-glass films: simulations meet experiments

In the last five years, a new experimental protocol, introduced by the Austin group has challenged theorists. Indeed, by studying the time growth of spin-glass correlation length on multilayer samples of thin film, the lower critical dimension has been measured experimentally [S. Guchhait and R. L. Orbach Phys. Rev. Lett. 112, (2014) 126401] and precision measurements of the aging rate have been obtained [Q. Zhai et al. Phys. Rev. B 95 (2017) 054304, S. Guchhait and R. L. Orbach Phys. Rev. Lett. 118,(2017) 157203]. The above experimental success clearly shows that playing with the sample geometry is a powerful tool. Nevertheless, this tool has been mostly disregarded by theorists, up to now. In my Ph.D. thesis, I deeply investigated the equilibrium properties and the aging dynamics of spin-glasses with film geometry. We carried on massive computer simulations and implemented our programs for a high level of parallelism and exploiting the power of last-generation chips, as the multi-thread options or alignments of many bits in a single computer word (SEE2). We used mainly two algorithms: the Parallel Tempering (PT) for the equilibrium investigation and the Metropolis single step for the out-equilibrium regime. Moreover, we implemented the performance of them using two different multispin codings: MUlti SAmple multispin coding (MUSA) and MUlti Site mutispin coding (MUSI). The MUSA algorithm is based on the representation of many samples system in a single computer word; instead, the MUSI one represents many spins of the same replica in a single computer word. The film geometry gives us the possibility to achieve equilibrium for temperature close to the 3D critical one in an easier way than a pure 3D system. We studied the static behavior of thin glassy films at the bulk critical temperature for several thickness and lattice values. Exploiting a Finite-Size Scaling (FSS) approach, we confirmed that a glassy film belongs to the same universality class of a bulk system. Then, we focused on the same quantity considered in experiments, namely the time-growing spin glass correlation length. The central hypothesis behind the experimental analysis, never verified before in a thorough theoretical study, is the existence of a dimensional crossover when the correlation length reaches the film width, followed by a dynamical arrest. We have simulated the spin-glass dynamics in films of varying width in all the relevant dynamic regimes, from picoseconds to equilibrium, for several temperatures. We confirmed the existence of a dimensional crossover from 3D to 2D dynamics that starts when the correlation length becomes comparable to the film thickness. We discovered rich dynamics that consist of four dynamical regimes regulated by the film width. Although the picture used by experimentalists of a complete dynamical arrest is an oversimplification, the basic hypothesis in their analysis is confirmed. In addition, we numerically implement, on the Ising spin glass, exploiting the super-computer Janus II, the seminal experimental protocol of the Zero-Field Cooling (ZFC) . The initial random spin configuration is placed instantaneously at the working temperature T and left to relax for a time tw, with zero external magnetic fields. At time tw, the external magnetic field is turned on and we started recording the magnetic density. Our analysis unveils a new scaling law describing how the magnetic response depends both on the applied magnetic field and on the size of the correlation length of the magnetic domains. Exploiting the Fisher-Sompolinsky relation, we could compare our numerical results to the experimental ones. Hence, we obtained a significant agreement between numerical and experimental results and we solved a tree-decades-old controversy about the nature of the Zeeman energy.