Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

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Abstract

We investigate the Ising model in one, two, and three dimensions using a cumulant method that allows us to determine the Lee-Yang zeros from the magnetization fluctuations in small lattices. By doing so with increasing system size, we are able to determine the convergence point of the Lee-Yang zeros in the thermodynamic limit and thereby predict the occurrence of a phase transition. The cumulant method is attractive from an experimental point of view since it uses fluctuations of measurable quantities, such as the magnetization in a spin lattice, and it can be applied to a variety of equilibrium and nonequilibrium problems. We show that the Lee-Yang zeros encode important information about the rare fluctuations of the magnetization. Specifically, by using a simple ansatz for the free energy, we express the large-deviation function of the magnetization in terms of Lee-Yang zeros. This result may hold for many systems that exhibit a first-order phase transition.
Original languageEnglish
Article number174418
Number of pages12
JournalPhysical Review B
Volume102
Issue number17
DOIs
Publication statusPublished - 12 Nov 2020
MoE publication typeA1 Journal article-refereed

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