کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4649285 1632437 2010 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A little statistical mechanics for the graph theorist
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
A little statistical mechanics for the graph theorist
چکیده انگلیسی

In this survey, we give a friendly introduction from a graph theory perspective to the qq-state Potts model. The Potts model is an important statistical mechanics tool for analyzing complex systems in which nearest neighbor interactions determine the aggregate behavior of the system. We present the surprising equivalence of the Potts model partition function and one of the most renowned graph invariants, the Tutte polynomial. This relationship has resulted in a remarkable synergy between the two fields of study. We highlight some of these interconnections, such as computational complexity results that have alternated between the two fields. The Potts model captures the effect of temperature on the system and plays an important role in the study of thermodynamic phase transitions. We discuss the equivalence of the chromatic polynomial and the zero-temperature antiferromagnetic partition function, and how this has led to the study of the complex zeros of these functions. We also briefly describe Monte Carlo simulations commonly used for Potts model analysis of complex systems. The Potts model has applications in areas as widely varied as magnetism, tumor migration, foam behaviors, and social demographics, and we provide a sampling of these that also demonstrates some variations of the Potts model. We conclude with some current areas of investigation that emphasize graph theoretic approaches.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 310, Issues 13–14, 28 July 2010, Pages 2037–2053
نویسندگان
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