Memory features in the random bond ising model

Nature exhibits memory formation in a myriad of ways. Memory formation under cyclic training has gained interest in recent years owing to its connection to reservoir computing. While a large body of simulation studies and experiments involving memory formation in glassy systems under periodic driving exists, this dissertation attempts to identify universal features by studying a much simpler model, the Nonequilibrium Random Bond Ising Model (NRBIM). This dissertation consists of three sets of simulations that uncover the memory properties arising through the periodic driving of magnetic systems. The first work explores Ising spins on a three-dimensional lattice under external driving. Critical exponents are extracted from avalanches and are shown to fall in the large universality class of the Nonequilibrium Random Field Ising Model. Novel scaling exponents related to memory are also summarized. Easily measured avalanche properties are shown to predict memory behavior. The second work comprises taking a more granular approach and studying the transition graphs of metastable mesostates formed under NRBIM. The differences between reversible and irreversible transitions are analyzed. It is concluded that transitions consisting of spins flipping opposite the direction of the changing field (backflips) are the primary cause of irreversible behavior under periodic driving. Moreover, those transitions with backflips that are reversible often obey the no-passing condition, which is often preserved in systems without frustration. Our simulation results offer insight into the capacity of a frustrated system to store multiple memories. The final study attempts to revisit the Sherrington-Kirkpatrick Spin Glass Model with the intent to study memory formation in a maximally frustrated system. The previously stated self-organizing critical behavior of avalanches in literature is found to be tuned-critical in reality. Systems of much smaller sizes in comparison to the three-dimensional RBIM systems are shown to need training cycles exceeding two orders of magnitude compared with the 3D spin systems. Memory-related exponents are obtained for the number of training cycles to reach a limit cycle and mismatch size distributions. The dissertation concludes with a discussion of the current state-of-the-art work on memory formation and an outlook on future directions.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Mansingh, Siddharth

Contributors dc:contributor

• Dahmen, Karin
• Bradlyn, Barry
• Hoffmann, Axel
• Goldschmidt, Elizabeth

• Memory
• Synchronization
• Spin-glass
• Trained Memory
• Limit Cycles

Statement dc:rights

• Copyright 2024 Siddharth Mansingh

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/127323

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F127323