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

Javier Moreno-Gordo

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

Javier Moreno-Gordo

Disordered Systems and Neural Networks · Submitted 7 Jul 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim However, without a doubt, the leitmotiv conducting this thesis is the role of numerical simulations as a valuable tool to explore spin-glass physics.

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arXiv ID2107.03276 (version 1)

Pith IDHPCLGHGB, Pith's permanent record of this paper and its review

CitationJavier Moreno-Gordo. "Deepening the knowledge of Spin Glasses: Metastate, Off-equilibrium phenomena and Temperature Chaos." arXiv:2107.03276 (2021). https://pith.science/paper/HPCLGHGB

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 10,677 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This thesis pretends to be another step in the development of numerical research in disordered systems.	background 0.54	0.09	0.02	hedged possibility 0.54
s1	Specifically, we will focus on spin glasses which have demonstrated to be a fertile field from both, experimental and theoretical approaches.	background 0.97	0.06	0.02	asserted 1.00
s2	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.	contribution 0.92	0.26	0.04	asserted 0.79
s3	However, without a doubt, the leitmotiv conducting this thesis is the role of numerical simulations as a valuable tool to explore spin-glass physics.	method 0.54	0.09	0.07	asserted 1.00
s4	This thesis is organized into five different parts.	background 0.48	0.25	0.01	asserted 1.00
s5	The first part, containing the Chapter 1, is focused on introducing the spin glasses to the reader.	background 0.63	0.14	0.01	asserted 1.00
s6	The second part, containing the Chapter 2, is dedicated to discussing the metastate.	contribution 0.63	0.16	0.02	asserted 0.90
s7	The third part, shaped by the Chapter 3 and Chapter 4, is devoted to studying the off-equilibrium dynamics in spin glasses.	contribution 0.71	0.19	0.02	asserted 0.89
s8	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.	contribution 0.80	0.24	0.03	asserted 0.99
s9	In Chapter 4 we will discuss an interesting phenomenon: the Mpemba effect.	contribution 0.79	0.25	0.02	asserted 0.78
s10	The fourth part, containing the Chapter 5, Chapter 6 and Chapter 7 is devoted to study the Temperature Chaos phenomenon in spin glasses.	contribution 0.66	0.13	0.02	asserted 0.96
s11	In Chapter 5 we introduce the main historical results on Temperature Chaos, from its origins to the last steps.	background 0.79	0.14	0.02	asserted 0.89
s12	In Chapter 6 we study equilibrated spin glasses and we characterize the Temperature Chaos from a static and a dynamical point of view.	contribution 0.96	0.75	0.03	asserted 0.98
s13	In Chapter 7 we tackle the problem of characterizing Temperature Chaos in off-equilibrium dynamics.	contribution 0.95	0.61	0.03	asserted 0.70
s14	The fifth and last part of the main body of the thesis corresponds to the conclusions.	background 0.47	0.14	0.04	asserted 0.99

What kind of paper the classifier reports this is: simulation study 0.94 · evidence from simulation or computation 0.96.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original 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.

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 33 sentences without a confident label

Builds on 2 papers

This work also extends the study of TCtemperature chaos performed in previous papers [ref] by the development of a variational methodvariational method.

Temperature chaos in 3D Ising Spin Glasses is driven by rare events · Last steps · 1.00
This work also extends the study of TCtemperature chaos performed in previous papers [ref] by the development of a variational methodvariational method.

Temperature chaos is a non-local effect · Last steps · 1.00

Uses the method or tool of 1 paper

We do so with the quotients methodquotients method [ref] which produces effective $ζ$ estimates at a well defined length scale.

New Universality Class in three dimensions: the Antiferromagnetic $RP^2$ model · The exponent $ζ$ · 1.00

Uses data or values from 1 paper

The computation of $θ$ have been performed numerically for $d=3$ resulting in $θ=0.27$ [ref] , $θ=0.26$ [ref] .

Stiffness of the Edwards-Anderson Model in all Dimensions · The Droplet picture · 0.99

Cites as support 2 papers

However, the TCtemperature chaos phenomenon represents a major obstacle in the performance of PT [ref] .

Temperature chaos in 3D Ising Spin Glasses is driven by rare events · Last steps · 0.96
Indeed, some experiments [ref] and most of the numerical work [ref] trying to simulate temperature-varyingtemperature-varying protocol experimental protocols can be interpreted as cumulative agingaging!cumulative.

Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model. II. Quasi-Equilibrium Regime of Spin Auto-Correlation Function · Memory and rejuvenation · 0.99

Cites as background 2 papers

It was in 2013 when the TCtemperature chaos was quantitatively studied as a rare-event-driven phenomenon [ref] .

Temperature chaos in 3D Ising Spin Glasses is driven by rare events · Last steps · 0.91
We stop here our brief recall of the RSBreplica!symmetry breaking (RSB) results in the SKSherrington-Kirkpatrick model, nonetheless, there exists a huge number of interesting results, for example in the rich physical interpretation (see e.g. [ref] ) or numerical results that agree with the RSBreplica!symmetry breaking (RSB) predictions [ref] .

Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model · Parisi's solution: the Replica Symmetry Breaking · 0.89

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