Random matrices and the six-vertex model
著者
書誌事項
Random matrices and the six-vertex model
（CRM monograph series, v. 32）
American Mathematical Society, c2014
大学図書館所蔵 件 / 全22件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 221-224)
内容説明・目次
内容説明
This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric.
「Nielsen BookData」 より