منابع مشابه
Lee-yang Problems and the Geometry of Multivariate Polynomials
We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by Pólya-Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee-Yang type problems in statistical mechanics, com...
متن کاملLecture 17: D-Stable Polynomials and Lee-Yang Theorems
Counting vs Sampling We called this course counting and sampling because of the equivalence theorem that we proved at the beginning of this course. All results that we proved using MCMC technique naturally give (approximate) sampler from our desired probability distributions. On the other hand, all results in the second part of the course naturally estimate the corresponding partition function ...
متن کاملCentral limit theorems, Lee-Yang zeros, and graph-counting polynomials
Article history: Received 4 September 2014 Available online 16 March 2016
متن کاملYang–Lee zeros of the Yang–Lee model
To understand the distribution of the Yang–Lee zeros in quantum integrable field theories we analyse the simplest of these systems given by the 2D Yang– Lee model. The grand-canonical partition function of this quantum field theory, as a function of the fugacity z and the inverse temperature β, can be computed in terms of the thermodynamics Bethe Ansatz based on its exact S-matrix. We extract t...
متن کاملLee-Yang theorem
In 1952, Lee and Yang published two important papers [1, 2] in statistical mechanics. They gave us a new way of looking at the nature of phase transitions, and suggested that we can regard partition functions as functions of external fields (in the case of Ising model, this would be magnetic fields), whose domains can be extended to the complex plane. In particular, they proved a series of Lee-...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2010
ISSN: 0003-486X
DOI: 10.4007/annals.2010.171.589