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Application of Integrable Systems to Phase Transitions

APPLICATION OF INTEGRABLE SYSTEMS TO PHASE TRANSITIONS

Mathematics

Mathematics & Science

Gt Product Group

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B2B GT

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B2B & B2C

The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems. Many new density models and free energy functions are consequently solved and presented. The phase transition models including critical phenomena with fractional power-law for the discontinuities of the free energies in the matrix models are systematically classified by means of a clear and rigorous mathematical demonstration. The methods here will stimulate new research directions such as the important Seiberg-Witten differential in Seiberg-Witten theory for solving the mass gap problem in quantum Yang-Mills theory. The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and Seiberg-Witten theory.

POST SECONDARY FOUR YEAR

COLFR

COLSO

COLJR

COLSR

Duration

Duration Unit Of Measure

Transaction Type

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
Dedication.
Preface.
Contents.
1: Introduction.
2: Densities in Hermitian Matrix Models.
3: Bifurcation Transitions and Expansions.
4: Large-N Transitions and Critical Phenomena.
5: Densities in Unitary Matrix Models.
6: Transitions in the Unitary Matrix Models.
7: Marcenko-Pastur Distribution and McKay&#x0027;s Law.
Some Integral Formulas.
Properties of the Elliptic Integrals.
Lax Pairs Based on the Potentials.
Hypergeometric-Type Differential Equations.
Index.

Application of Integrable Systems to Phase Transitions.css-1p8rvzy{position:absolute;padding-left:8px;}

Application of Integrable Systems to Phase Transitions