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Register a new userDeepening the knowledge of Spin Glasses: Metastate, Off-equilibrium phenomena and Temperature Chaos
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Added by
Javier Moreno-Gordo
Publication date
2021
fields
Physics
and research's language is
English
Authors
Javier Moreno-Gordo
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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.
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We find a dynamic effect in the non-equilibrium dynamics of a spin glass that closely parallels equilibrium temperature chaos. This effect, that we name dynamic temperature chaos, is spatially heterogeneous to a large degree. The key controlling quantity is the time-growing spin-glass coherence length. Our detailed characterization of dynamic temperature chaos paves the way for the analysis of recent and forthcoming experiments. This work has been made possible thanks to the most massive simulation to date of non-equilibrium dynamics, carried out on the Janus~II custom-built supercomputer.
We have introduced a variational method to improve the computation of integrated correlation times in the Parallel Tempering Dynamics, obtaining a better estimate (a lower bound, at least) of the exponential correlation time. Using this determination of the correlation times, we revisited the problem of the characterization of the chaos in temperature in finite dimensional spin glasses by means of the study of correlations between different chaos indicators computed in the static and the correlation times of the Parallel Tempering dynamics. The sample-distribution of the characteristic time for the Parallel Tempering dynamics turns out to be fat-tailed and it obeys finite-size scaling.
We study zero-temperature, stochastic Ising models sigma(t) on a d-dimensional cubic lattice with (disordered) nearest-neighbor couplings independently chosen from a distribution mu on R and an initial spin configuration chosen uniformly at random. Given d, call mu type I (resp., type F) if, for every x in the lattice, sigma(x,t) flips infinitely (resp., only finitely) many times as t goes to infinity (with probability one) --- or else mixed type M. Models of type I and M exhibit a zero-temperature version of ``local non-equilibration. For d=1, all types occur and the type of any mu is easy to determine. The main result of this paper is a proof that for d=2, plus/minus J models (where each coupling is independently chosen to be +J with probability alpha and -J with probability 1-alpha) are type M, unlike homogeneous models (type I) or continuous (finite mean) mus (type F). We also prove that all other noncontinuous disordered systems are type M for any d greater than or equal to 2. The plus/minus J proof is noteworthy in that it is much less ``local than the other (simpler) proof. Homogeneous and plus/minus J models for d greater than or equal to 3 remain an open problem.
Domain-wall free-energy $delta F$, entropy $delta S$, and the correlation function, $C_{rm temp}$, of $delta F$ are measured independently in the four-dimensional $pm J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $theta$, the fractal dimension of domain walls $d_{rm s}$ and the chaos exponent $zeta$ are extracted from the finite-size scaling analysis of $delta F$, $delta S$ and $C_{rm temp}$ respectively well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $zeta=d_{rm s}/2-theta$ derived by the droplet theory within our numerical accuracy. We also study bond chaos induced by random variation of bonds, and find that the bond and temperature perturbations yield the universal chaos effects described by a common scaling function and the chaos exponent. These results strongly support the appropriateness of the droplet theory for the description of chaos effect in the EA Ising spin glasses.
The aging in a Heisenberg-like spin glass Ag(11 at% Mn) is investigated by measurements of the zero field cooled magnetic relaxation at a constant temperature after small temperature shifts $|Delta T/T_g| < 0.012$. A crossover from fully accumulative to non-accumulative aging is observed, and by converting time scales to length scales using the logarithmic growth law of the droplet model, we find a quantitative evidence that positive and negative temperature shifts cause an equivalent restart of aging (rejuvenation) in terms of dynamical length scales. This result supports the existence of a unique overlap length between a pair of equilibrium states in the spin glass system.
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