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.

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 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 On sinh–Gordon thermodynamic Bethe ansatz and fermionic basis

2014 ◽  
Vol 29 (20) ◽  
pp. 1450111 ◽  
Author(s):  
Stefano Negro
Keyword(s):  
Bethe Ansatz ◽  
Thermodynamic Bethe Ansatz ◽  
The One

We review the construction of the fermionic basis for sinh–Gordon model and investigate numerically the ultraviolet limit of the one-point functions. We then compare the predictions obtained from this formalism against previously established results.

scholarly journals Analytical results of the one-dimensional Hubbard model in the high-temperature limit

2001 ◽  
Vol 64 (19) ◽  
Author(s):  
I. C. Charret ◽  
E. V. Corrêa Silva ◽  
S. M. de Souza ◽  
O. Rojas Santos ◽  
M. T. Thomaz ◽  
...  
Keyword(s):  
High Temperature ◽  
Hubbard Model ◽  
Temperature Limit ◽  
One Dimensional ◽  
High Temperature Limit ◽  
Analytical Results ◽  
The One

On the Law of Equipartition for Translational Motion of Excited Molecules in Equilibrium with Thermal Radiation

1989 ◽  
Vol 44 (4) ◽  
pp. 273-277
Author(s):  
B. H. Lavenda
Keyword(s):  
Translational Motion ◽  
Excited Molecule ◽  
Temperature Limit ◽  
Stimulated Emission ◽  
High Temperature Limit ◽  
Radiation Theory ◽  
The Law ◽  
Excited Molecules ◽  
The One ◽  
Limiting Condition

Abstract Einstein’s radiation theory consists of two parts: the derivation of Planck's radiation law from a physical mechanism of absorption and emission of radiation by excited molecules that are in thermal equilibrium with the radiation field and a demonstration of the validity of the law of equipartition of energy for the translational motion of the molecules. Several incongruities are observed: Einstein could not have legitimately substituted back into his dynamical equilibrium condition, valid at any finite temperature, a limiting condition between the coefficients of absorption and stimulated emission that he obtained in the high temperature limit. His justification of the law of equipartition involves, on the one hand, treating the motion of the excited molecule as brownian motion while, on the other hand, employing special relativity to obtain an expression for the diffusion coefficient. In the former the velocity of the molecule is a stochastic variable while in the latter it is a uniform velocity. Hence equipartition does not hold for the translational motion.

scholarly journals Thermal effects of a photon gas with a deformed Heisenberg algebra

2016 ◽  
Vol 31 (32) ◽  
pp. 1650172 ◽  
Author(s):  
R. Bufalo
Keyword(s):  
High Temperature ◽  
Thermal Effects ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Temperature Limit ◽  
Loop Order ◽  
High Temperature Limit ◽  
Photon Gas ◽  
The One ◽  
Boltzmann Law

In this paper, we have considered the thermodynamics of a photon gas subject to the presence of a minimal measurable length following from a covariant extension of the original generalized uncertainty principle (GUP). After consistently establishing a generalized dynamics, we define a GUP deformed Maxwell invariant which serves as the basis for our study. In order to highlight the GUP effects, we compute the one- and two-loop order contribution to the partition function at the high-temperature limit. Afterwards, by computing the internal energy density, we conclude that the additional terms can be seen as corrections [Formula: see text] to the Stefan–Boltzmann law due to GUP effects.

scholarly journals Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Lucía Córdova ◽  
Stefano Negro ◽  
Fidel I. Schaposnik Massolo
Keyword(s):  
Bethe Ansatz ◽  
Bound States ◽  
Turning Point ◽  
Central Charge ◽  
Continuation Method ◽  
Complex Conjugate ◽  
Minimal Models ◽  
Thermodynamic Bethe Ansatz ◽  
New Family ◽  
The Difference

Abstract We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T$$ \overline{\mathrm{T}} $$ T ¯ deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number k of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As k → ∞ the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S-matrices describing the Φ1,3 integrable deformation of non-unitary minimal models $$ \mathcal{M} $$ M 2,2n+3.

scholarly journals LOGARITHMIC CORRECTION TO SCALING FOR MULTISPIN STRINGS IN THE AdS5 BLACK HOLE BACKGROUND

2008 ◽  
Vol 23 (05) ◽  
pp. 719-727
Author(s):  
A. L. LARSEN
Keyword(s):  
Black Hole ◽  
Radial Direction ◽  
Temperature Limit ◽  
Space Time ◽  
Explicit Solutions ◽  
Logarithmic Correction ◽  
High Temperature Limit ◽  
Black Hole Background ◽  
Correction To Scaling ◽  
The One

We find new explicit solutions describing closed strings spinning with equal angular momentum in two independent planes in the AdS5 black hole space–time. These are 2n-folded strings in the radial direction and also winding m times around an angular direction. We specially consider these solutions in the long string and high temperature limit, where it is shown that there is a logarithmic correction to the scaling between energy and spin. This is similar to the one-spin case. The strings are spinning, or actually orbiting around the black hole of the AdS5 black hole space–time, similar to the solutions previously found in black hole space–times.

SINE–GORDON THEORY IN THE REPULSIVE REGIME, THERMODYNAMIC BETHE ANSATZ AND MINIMAL MODELS

2012 ◽  
Vol 26 (27n28) ◽  
pp. 1243011
Author(s):  
H. ITOYAMA
Keyword(s):  
Bethe Ansatz ◽  
Central Charge ◽  
Thirring Model ◽  
Minimal Models ◽  
Massless Limit ◽  
Thermodynamic Bethe Ansatz ◽  
Massive Thirring Model ◽  
Conformal Theory

Neutral excitations present in the repulsive regime (1/2 < β2/8π < 1) of the sine–Gordon/massive–Thirring model and its study of the massless limit by the thermodynamic Bethe ansatz is revisited. At β2/8π = 1-1/(p+1) the solitons become infinitely heavy, forcing truncation to the neutral excitations alone. The central charge in this limit is calculated to be c = 1-6/p(p+1); the mass and S-matrices of the truncated theories are identified as those of the minimal conformal theory Mp perturbed by the ϕ(1, 3) operator.

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