A Finite-temperature Phase Transition for the Ising Spin-glass in $d\geq 2$

arXiv2105.01188MaRDI QIDQ6366746

Yan Ru Pei, Massimiliano Di Ventra

Publication date: 3 May 2021

Abstract: It is believed that the $pmJ$ Ising spin-glass does not order at finite temperatures in dimension $d=2$. However, using a graphical representation and a contour argument, we prove rigorously the existence of a finite-temperature phase transition in $dgeq2$ with $T_{c}geq0.4$. 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.

Has companion code repository: https://github.com/PeaBrane/Ising-Simulation

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Signed and weighted graphs (05C22)

This page was built for publication: A Finite-temperature Phase Transition for the Ising Spin-glass in $d\geq 2$