A Finite-temperature Phase Transition for the Ising Spin-glass in $d\geq 2$
Abstract
It is believed that the Ising spin-glass does not order at finite temperatures in dimension . However, using a graphical representation and a contour argument, we prove rigorously the existence of a finite-temperature phase transition in with . In the graphical representation, the low-temperature phase allows for the coexistence of multiple infinite clusters each with a rigidly aligned spin-overlap state. These clusters correlate negatively with each other, and are entropically stable without breaking any global symmetry. They can emerge in most graph structures and disorder measures.
Keywords
Cite
@article{arxiv.2105.01188,
title = {A Finite-temperature Phase Transition for the Ising Spin-glass in $d\geq 2$},
author = {Yan Ru Pei and Massimiliano Di Ventra},
journal= {arXiv preprint arXiv:2105.01188},
year = {2022}
}
Comments
The proof of the finitude of zero-energy contours in Appendix D.2 contains a technical error, where we failed to notice that opening a red bond in any of the four quadrants can possibly restrict opening of any blue bonds in the contour. This means that the probability that the contour is zero-energy (no blue-bonds) cannot be bounded exponentially, thus the result does not immediately follow