Tag Archives: isingmodel

Title page of Ising model paper

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

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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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Just presented at the Annual Meeting of the Physical Society of Taiwan

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I just presented a talk “Quenching to field-stabilized magnetization plateaus in the unfrustrated Ising antiferromagnet” based on my preprint that I posted on arXiv last week at the Annual Meeting of the Physical Society of Taiwan at National Pingtung University in Pingtung, Taiwan. I haven’t gotten around to making a post about this paper yet (that is coming soon), but in the meantime I will post my slides from this talk here. My slides included some movies of the process of freezing in to magnetization plateaus. Since PDFs can’t include movies I will post the movies below.

Gif of Ising spin configurations arriving at a frozen plateau state.
The spin configuration over time starting from a random (T=∞) state and doing single spin flip Metropolis updates at T=0 and h=1 until we arrive at a final frozen state. Individual spin states are denoted by the (+) and (-); the background shading shows which of the antiferromagnetic ground states each site is in. In the final frozen state the domain walls are all straight lines or corners with (+) on the inside.

Gif of Ising spin configurations arriving at a frozen plateau state.
The spin configuration over time starting from a random (T=∞) state and doing single spin flip Metropolis updates at T=0 and h=3 until we arrive at a final frozen state. Individual spin states are denoted by the (+) and (-); the background shading shows which of the antiferromagnetic ground states each site is in. In the final frozen state the domain walls are all diagonal or square-wave-like with excess (+) spin.