Sorin Istrail's Homepage :: Research Interests

Statistical Mechanics

"A theory is the more impressive the greater the simplicity of its premises is, the more different kind of things it relates, and the more extended its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will bever be overthrown."
Albert Einstein (1970)

The Problem.

I am interested in developing mathematical and computer science theory unvailing provable combinatorics roots of phase transition in statistical mechanics. Provable results on computational complexity should lead the way to avenues for the development of tractable algorithms for the discovery of phase thransition critical points. We are using computational complexity methods to unify similar state-of-the-art analytical analyses of statistical mechanics models such as Ising, Dimers, Ice and Percolation. In these models, exactly solved particular planar models were found, while NO three-dimensional exactly solved model has been ever found for either of them.

For the Ising Model, we have obtained Theorems that provide such "qualitative" solutions for variants of the three-dimensional Ising model. Our results focus on the set of finite sublattices of an (infinite) crystal lattice subject to various symmetry groups.

Our work on the Statistical Mechanics of the Ising model got media attention


Our STOC 2000 Paper:

Media Coverage

Intro to the Ising Model

 

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