Deepening the knowledge of Spin Glasses: Metastate, Off-equilibrium phenomena and Temperature Chaos

Abstract

This thesis pretends to be another step in the development of numerical research in disordered systems. Specifically, we will focus on spin glasses which have demonstrated to be a fertile field from both, experimental and theoretical approaches. Throughout this thesis, we will discuss a variety of interesting phenomenons and we will also open new avenues to previously unexplored effects in the context of spin glasses. However, without a doubt, the leitmotiv conducting this thesis is the role of numerical simulations as a valuable tool to explore spin-glass physics. This thesis is organized into five different parts. The first part, containing the Chapter 1, is focused on introducing the spin glasses to the reader. The second part, containing the Chapter 2, is dedicated to discussing the metastate. The third part, shaped by the Chapter 3 and Chapter 4, is devoted to studying the off-equilibrium dynamics in spin glasses. Specifically, Chapter 3 is focused on discussing the growth of the coherence length in spin glasses, a key quantity that characterizes the off-equilibrium evolution of those systems. In Chapter 4 we will discuss an interesting phenomenon: the Mpemba effect. The fourth part, containing the Chapter 5, Chapter 6 and Chapter 7 is devoted to study the Temperature Chaos phenomenon in spin glasses. In Chapter 5 we introduce the main historical results on Temperature Chaos, from its origins to the last steps. In Chapter 6 we study equilibrated spin glasses and we characterize the Temperature Chaos from a static and a dynamical point of view. In Chapter 7 we tackle the problem of characterizing Temperature Chaos in off-equilibrium dynamics. The fifth and last part of the main body of the thesis corresponds to the conclusions.

Ph.D Thesis defended at the University of Zaragoza on the 21th of June of 2021

References in corpus (13)

• Supercooled Liquids for Pedestrians
• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Fractal free energy landscapes in structural glasses
• Exponentially faster cooling in a colloidal system
• Make life simple: unleash the full power of the parallel tempering algorithm
• Simulating spin systems on IANUS, an FPGA-based computer
• The correspondence between long-range and short-range spin glasses
• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Testing statics-dynamics equivalence at the spin-glass transition in three dimensions
• On the Slowing Down of Spin Glass Correlation Length Growth:simulations meet experiments
• Tethered Monte Carlo: computing the effective potential without critical slowing down
• Mean-value identities as an opportunity for Monte Carlo error reduction
• Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions