Thermodynamic Bethe Ansatz

2020 ◽  
pp. 791-835
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Bethe Ansatz ◽  
Free Field ◽  
Integrable Model ◽  
Finite Size ◽  
Casimir Energy ◽  
Thermodynamic Bethe Ansatz ◽  
Channel Quantization ◽  
Bulk Energy ◽  
Energy And Momentum

The Thermodynamic Bethe Ansatz (TBA) allows us to study finite size and finite temperature effects of an integrable model. This chapter investigates the integral equations that determine the free energy and gives their physical interpretation. It discusses Casimir energy, Bethe relativistic wave function, the derivation of thermodynamics, the meaning of pseudo-energy (dressed energy and momentum), infrared and ultraviolet limits, the coefficient of bulk energy, the general form of the TBA equations, the thermodynamics of the free field theories, L-channel quantization and the LeClair–Mussardo formula. It also covers the application of the Yang–Lee S-matrix, the magnetic field Ising model, and the tricritical Ising model.

THE CRITICAL BEHAVIOR OF SINE-GORDON MODEL

1992 ◽  
Vol 06 (11) ◽  
pp. 665-674
Author(s):  
YI-MIN LIU ◽  
FU-CHO PU ◽  
HANG SU
Keyword(s):  
Bethe Ansatz ◽  
Excited States ◽  
Critical Behavior ◽  
Coupling Parameter ◽  
Finite Size ◽  
Conformal Anomaly ◽  
Critical Coupling ◽  
Sine Gordon Model ◽  
Energy And Momentum ◽  
Finite Size Corrections

Using the algebraic Bethe Ansatz and Euler-Maclaurin formulae, we calculate the finite-size corrections to the energy and momentum of ground and excited states for the sine-Gordon model. The conformal anomaly, operator dimension and critical coupling parameter are given in the ultraviolet limit.

scholarly journals Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bao-ning Du ◽  
Min-xin Huang
Keyword(s):  
Large Class ◽  
Bethe Ansatz ◽  
Difference Equations ◽  
The Other ◽  
Elementary Functions ◽  
Quantum Dilogarithm ◽  
Thermodynamic Bethe Ansatz ◽  
Dilogarithm Function ◽  
Quantum Operators

Abstract We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

scholarly journals Analytical expressions for a finite-size 2D Ising model

2017 ◽  
Vol 26 (3) ◽  
pp. 165-171 ◽  
Author(s):  
I. M. Karandashev ◽  
B. V. Kryzhanovsky ◽  
M. Yu. Malsagov
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Analytical Expressions

scholarly journals Finite-size behavior of the critical Ising model on a rectangle with free boundaries

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
Xintian Wu ◽  
Nickolay Izmailian ◽  
Wenan Guo
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Free Boundaries
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