scholarly journals Extreme eigenvalue distributions of Jacobi ensembles: New exact representations, asymptotics and finite size corrections

2019 ◽  
Vol 947 ◽  
pp. 114724 ◽  
Author(s):  
Laureano Moreno-Pozas ◽  
David Morales-Jimenez ◽  
Matthew R. McKay
Keyword(s):  
Finite Size ◽  
Extreme Eigenvalue ◽  
Finite Size Corrections

scholarly journals Finite-size corrections to the rotating string and the winding state

2008 ◽  
Vol 2008 (08) ◽  
pp. 099-099 ◽  
Author(s):  
Davide Astolfi ◽  
Troels Harmark ◽  
Gianluca Grignani ◽  
Marta Orselli
Keyword(s):  
Finite Size ◽  
Rotating String ◽  
Finite Size Corrections

Finite Heisenberg Quantum Spin Chain

2019 ◽  
pp. 667-686
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Conformal Symmetry ◽  
Finite Size ◽  
Quantum Spin ◽  
Ansatz Method ◽  
Finite Sums ◽  
Mathematical Techniques ◽  
Higher Order Corrections ◽  
Finite Size Corrections ◽  
Maclaurin Formula

The Bethe ansatz genuinely considers a finite system. The extraction of finite-size results from the Bethe ansatz equations is of genuine interest, especially against the background of the results of finite-size scaling and conformal symmetry in finite geometries. The mathematical techniques introduced in chapter 19 permit a systematic treatment in this chapter of finite-size corrections as corrections to the thermodynamic limit of the system. The application of the Euler-Maclaurin formula transforming finite sums into integrals and finite-size corrections transforms the Bethe ansatz equations into Wiener–Hopf integral equations with inhomogeneities representing the finite-size corrections solvable using the Wiener–Hopf technique. The results can be compared to results for finite systems obtained from other approaches that are independent of the Bethe ansatz method. It briefly discusses higher-order corrections and offers a general assessment of the finite-size method.

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