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

Autor: Deger, Aydin, Brange, Fredrik, Flindt, Christian
Rok vydání: 2020
Předmět:
Zdroj: Phys. Rev. B 102, 174418 (2020)
Druh dokumentu: Working Paper
DOI: 10.1103/PhysRevB.102.174418
Popis: 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 non-equilibrium 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.
Comment: 13 pages, 8 figures, final version
Databáze: arXiv