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

Editors’ Suggestion: Phys. Rev. B 102, 174418 (2020)

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.

arXiv:2006.15125

Show BibTeX: @article{Deger2020b,
title = {{L}ee-{Y}ang theory, high cumulants, and large-deviation statistics of the magnetization in the {I}sing model},
author = {Deger, Aydin and Brange, Fredrik and Flindt, Christian},
journal = {Phys. Rev. B},
volume = {102},
issue = {17},
pages = {174418},
numpages = {12},
year = {2020},
month = {Nov},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.102.174418},
url = {https://link.aps.org/doi/10.1103/PhysRevB.102.174418}}

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