Category Archives: ising

screenshot of Bulletin of APS March Meeting

Watch my talk at the March Meeting Thursday 9:12 am central time

Tomorrow (Thursday 3/18) I’m giving my talk at the March Meeting!

R20.00005: Field-induced freezing in the unfrustrated Ising antiferromagnet
Thursday, March 18, 9:12 AM–9:24 AM CDT
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We study instantaneous quenches from infinite temperature to well below Tc in the two-dimensional (2D) square lattice Ising antiferromagnet in the presence of a longitudinal external magnetic field. Under single-spin-flip Metropolis algorithm Monte Carlo dynamics, this protocol produces a pair of metastable magnetization plateaus that prevent the system from reaching the equilibrium ground state except for some special values of the field. This occurs despite the absence of intrinsic disorder or frustration. We explain the plateaus in terms of local spin configurations that are stable under the dynamics. Although the details of the plateaus depend on the update scheme, the underlying principle governing the breakdown of ergodicity is quite general and provides a broader paradigm for understanding failures of ergodicity in Monte Carlo dynamics. See also: Iaizzi, Phys. Rev. E 102 032112 (2020), doi:10.1103/PhysRevE.102.032112

*Note: The views expressed here are the speaker’s, and do not necessarily represent the positions or policies of the AAAS STPF Program, the US Dept. of Energy, or the US Government.

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Title page of Ising model paper

Just published: field-stabilized frozen states in the AFM Ising model

I’m thrilled to announce that my first single-author paper has just been published in Physical Review E:

Field-induced freezing in the unfrustrated Ising antiferromagnet
Adam Iaizzi,
Physical Review E 102, 032112 (2020) [paywall] 
[free PDF] [arXiv]

This paper is a continuation of the theme of my research career, which could be loosely described: “try adding a magnetic field to an antiferromagnet and see if something interesting happens.” In this case, I added a magnetic field to the classical 2D Ising antiferromagnet and studied it with the simplest implementation of Monte Carlo: the Metropolis(-Rosenbluth-Teller) algorithm. At low temperatures I found that simulations never reached the ground state. Instead, they get trapped in local energy minima from which they never escape: frozen states with finite magnetization. There are so many of these frozen states available that you are effectively guaranteed to cross one before you can reach the correct ground state. These frozen states can be described by simple rules based on stable local configurations.

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