scholarly journals THERMODYNAMIC BETHE ANSATZ EQUATION FOR osp(1|2) INTEGRABLE SPIN CHAIN

1999 ◽  
Vol 14 (35) ◽  
pp. 2427-2435 ◽  
Author(s):  
KAZUMITSU SAKAI ◽  
ZENGO TSUBOI
Keyword(s):  
Free Energy ◽  
Low Temperature ◽  
Bethe Ansatz ◽  
Infinite Number ◽  
Spin Chain ◽  
Lie Superalgebra ◽  
Temperature Limit ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz ◽  
Integrable Spin

The thermodynamic Bethe ansatz is applied to a quantum integrable spin chain associated with the Lie superalgebra osp (1|2). Using the string hypothesis, we derive a set of infinite number of nonlinear integral equations (thermodynamic Bethe ansatz equation), which characterize the free energy. The low temperature limit of the free energy is also discussed.

scholarly journals THERMODYNAMIC BETHE ANSATZ EQUATION FROM FUSION HIERARCHY OF osp(1|2) INTEGRABLE SPIN CHAIN

2000 ◽  
Vol 15 (15) ◽  
pp. 2329-2346 ◽  
Author(s):  
KAZUMITSU SAKAI ◽  
ZENGO TSUBOI
Keyword(s):  
Free Energy ◽  
Excited State ◽  
Bethe Ansatz ◽  
Spin Chain ◽  
Lie Superalgebra ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz ◽  
Functional Relations ◽  
Integrable Spin ◽  
T System

The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp (1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of the QTM and derive the functional relations among them (T-system) and their certain combinations (Y-system). Their analytical property leads to the nonlinear integral equations which describe the free energy and the correlation length at any finite temperatures. With regard to the free energy, they coincide with the TBA equation based on the string hypothesis.

scholarly journals A NOTE ON THE osp(1|2s) THERMODYNAMIC BETHE ANSATZ EQUATION

2002 ◽  
Vol 17 (17) ◽  
pp. 2351-2368 ◽  
Author(s):  
ZENGO TSUBOI
Keyword(s):  
Bethe Ansatz ◽  
Central Charge ◽  
Lie Superalgebra ◽  
Temperature Limit ◽  
Entropy Density ◽  
Fundamental Representation ◽  
Thermodynamic Bethe Ansatz ◽  
High Temperature Limit ◽  
The One ◽  
T System

A Bethe ansatz equation associated with the Lie superalgebra osp(1|2s) is studied. A thermodynamic Bethe ansatz (TBA) equation is derived by the string hypothesis. The high temperature limit of the entropy density is expressed in terms of the solution of the osp(1|2s) version of the Q-system. In particular for the fundamental representation case, we also derive a TBA equation from the osp(1|2s) version of the T-system and the quantum transfer matrix method. This TBA equation is identical to the one from the string hypothesis. The central charge is expressed by the Rogers dilogarithmic function and identified to s.

Thermodynamics of the Isotropic Heisenberg Quantum Spin Chain

2019 ◽  
pp. 641-654
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Free Energy ◽  
Bethe Ansatz ◽  
Finite Temperature ◽  
Spin Chain ◽  
Conformal Symmetry ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
Explicit Formulas ◽  
Thermodynamic Bethe Ansatz ◽  
Physical Quantities

This chapter presents the extension of the Bethe ansatz to finite temperature, the thermodynamic Bethe ansatz, for the antiferromagnetic isotropic Heisenberg quantum spin chain, the XXX quantum spin chain. It discusses how the added complications of this model arise from the more complicated structure of excitations of the quantum spin chain, the complex string excitations, which have to be included in the Bethe ansatz thermodynamics. It derives the integral equations of the thermodynamic Bethe ansatz for the XXX quantum spin chain and mentions explicit formulas for the free energy of the quantum spin chain and some interesting physical quantities, especially making contact with predictions of conformal symmetry.

The Thermodynamic Bethe Ansatz and a Connection with Painlevé Equations

1997 ◽  
Vol 11 (01n02) ◽  
pp. 69-74
Author(s):  
Craig A. Tracy ◽  
Harold Widom
Keyword(s):  
Integral Equations ◽  
Bethe Ansatz ◽  
Painlevé Equations ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz ◽  
Painleve Equations ◽  
Linear Integral ◽  
Linear Integral Equations

We summarize some recent connections between a class of nonlinear integral equations related to the thermodynamic Bethe Ansatz and a class of linear integral equations related to the Painlevé equations.

scholarly journals Generalized Exclusion Statistics in the Kondo Problem

1997 ◽  
Vol 11 (07) ◽  
pp. 283-292 ◽  
Author(s):  
A. P. Protogenov ◽  
V. A. Verbus
Keyword(s):  
Phase Shift ◽  
Low Temperature ◽  
Bethe Ansatz ◽  
Multicomponent System ◽  
Scattering Matrix ◽  
Exclusion Principle ◽  
Kondo Problem ◽  
Universal Form ◽  
Thermodynamic Bethe Ansatz ◽  
System Of Particles

We consider the generalized exclusion statistics in the Kondo problem. The thermodynamic Bethe ansatz equations have been used for a multicomponent system of particles obeying the generalized exclusion principle. We have found a relation between the derivative of the phase shift of the scattering matrix for Fermi particles and for particles characterized by generalized exclusion statistics. We show that the statistical matrix in the Kondo problem has a universal form in the high and low temperature limits.

Low-temperature limit of the rate of propagation of chains in the hydrobromination of ethylene

1979 ◽  
Vol 76 ◽  
pp. 1013-1015 ◽  
Author(s):  
D.P. Kiryukhin ◽  
I.M. Barkalov ◽  
V.l. Goldanskii
Keyword(s):  
Low Temperature ◽  
Temperature Limit

scholarly journals A 4d $$ \mathcal{N} $$ = 1 Cardy Formula

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Jaewon Song
Keyword(s):  
Black Holes ◽  
Free Energy ◽  
Asymptotic Behavior ◽  
High Temperature ◽  
Gauge Theory ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Superconformal Index ◽  
High Temperature Limit ◽  
Cardy Formula

Abstract We study the asymptotic behavior of the (modified) superconformal index for 4d $$ \mathcal{N} $$ N = 1 gauge theory. By considering complexified chemical potential, we find that the ‘high-temperature limit’ of the index can be written in terms of the conformal anomalies 3c − 2a. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 < a/c < 3/2 for the interacting SCFT is satisfied. We study $$ \mathcal{N} $$ N = 1 theories that are dual to AdS5 × Yp,p and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

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