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

2013 ◽  
pp. 161-169
Author(s):  
H. ITOYAMA
Keyword(s):  
Bethe Ansatz ◽  
Minimal Models ◽  
Thermodynamic Bethe Ansatz

scholarly journals INTEGRABLE PERTURBATIONS OF CFT WITH COMPLEX PARAMETER: THE M3/5 MODEL AND ITS GENERALIZATIONS

1996 ◽  
Vol 11 (04) ◽  
pp. 677-697 ◽  
Author(s):  
F. RAVANINI ◽  
M. STANISHKOV ◽  
R. TATEO
Keyword(s):  
Bethe Ansatz ◽  
Minimal Model ◽  
Previous Literature ◽  
Coupling Constant ◽  
Minimal Models ◽  
Thermodynamic Bethe Ansatz ◽  
Bare Coupling ◽  
Bare Coupling Constant ◽  
Ansatz Approach ◽  
Relevant Operator

By using the thermodynamic Bethe ansatz approach, we give evidence of the existence of both massive and massless behaviors for the ϕ2,1 perturbation of the M3,5 nonunitary minimal model, thus resolving apparent contradictions in the previous literature. The two behaviors correspond to changing the perturbing bare coupling constant from real values to imaginary ones. Generalizations of this picture to the whole class of nonunitary minimal models Mp,2p±1, perturbed by their least relevant operator, lead to a cascade of flows similar to that of unitary minimal models perturbed by ϕ1,3. Various aspects and generalizations of this phenomenon and the links with the Izergin–Korepin model are discussed.

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.

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.

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.

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.

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