Titlebook: Application of Integrable Systems to Phase Transitions; C.B. Wang Book 2013 Springer-Verlag Berlin Heidelberg 2013 Integrable system.Large

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Introduction,he hypergeometric-type differential equations improve on some shortages of integrable systems to work on physical problems, such as the fact that a soliton system does not have a differential equation along the spectrum direction, and illustrate a new background to study the singularities of physica

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Bifurcation Transitions and Expansions,rom the string equations. The density on multiple disjoint intervals for higher degree potential and the corresponding free energy are discussed in association with the Seiberg-Witten differential. In the symmetric cases for the quartic potential, the third-order phase transitions are explained with

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Densities in Unitary Matrix Models, the orthogonal polynomials on the unit circle. The integrable systems and string equation discussed in this chapter provide a structure for finding the generalized density models and parameter relations that will be used as the mathematical foundation to investigate the transition problems discusse

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theory. The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and Seiberg-Witten theory..978-3-642-44024-3978-3-642-38565-0

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