Chula Intelligent and Complex Systems - CHICS

Special seminar on Quantum Topological Data Analysis on this Friday afternoon in Room 610, Mahamakut Building (Faculty of Science).

No prior knowledge in quantum computation is assumed.

From Nishimori himself.

“This may be one of the most significant papers in my 45-year career in the statistical physics of spin glasses. It paves the way for analytically addressing two long-standing issues: (i) the applicability of mean-field predictions (the Parisi solution) to the realistic finite-dimensional system (the Edwards-Anderson model), and (ii) the existence of temperature chaos in the Edwards-Anderson model.

Immediately after posting it on arXiv, I received a message from a prominent researcher of spin glass theory, saying "Congratulations. It is very deep and insightful. I am sure I will keep thinking about it for a long time."

This paper introduces strong correlations among disorder variables in the Ising spin glass, in contrast to the standard Edwards-Anderson model, which assumes independently-distributed disorder. The first major result is a proof that, on the Nishimori line, magnetization exhibits support on a finite interval -- meaning it can vary significantly across different disorder realizations -- if the Edwards-Anderson model undergoes Parisi-type replica symmetry breaking. This highly unusual result challenges the conventional understanding that replica symmetry breaking does not occur on the Nishimori line. Alternatively, it may indicate that there is no replica symmetry breaking in the Edwards-Anderson model.

Additionally, this paper shows that a ferromagnetic phase can only exist on the Nishimori line if temperature chaos is present in the Edwards-Anderson model. Intuitively, the restriction of the ferromagnetic phase to a single line appears highly improbable, though a formal proof remains elusive. This finding marks a step toward resolving the long-debated issue of temperature chaos in the Edwards-Anderson model.

I expect active developments along the lines opened up in this paper.

I was able to pursue this study after retiring from all goal-oriented projects (mostly on quantum stuff). The Institute of Science Tokyo (formerly Tokyo Institute of Technology) has provided generous support, enabling me to devote myself full-time to blue-sky research on a problem I've long wanted to explore out of pure academic curiosity.”

Anomalous distribution of magnetization in an Ising spin glass with correlated disorder The effect of correlations in disorder variables is a largely unexplored topic in spin glass theory. We study this problem through a specific example of correlated disorder introduced in the Ising spin glass model. We prove that the distribution function of the magnetization along the Nishimori line...