Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries

O’Brien, Denis; Pearce, Paul A.; Warnaar, S. Ole

doi:10.1016/s0550-3213(97)00424-0

Cited by 26 publications

(80 citation statements)

References 31 publications

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“…A 2-string is a pair of zeros (u j , u The relations [20] between these numbers determining the string content take the form of an (m, n)-system [21,22] …”

Section: Classification: (M N) Systems and Quantum Numbersmentioning

confidence: 99%

“…Bringing the location of a 1-string closer to the real axis by interchanging the location of the 1-string with a 2-string increments its quantum number by one unit and increases the energy. At the tricritical point where R = 0 these jumps in energy are quantised in a tower with energy levels given by [20] …”

Section: Classification: (M N) Systems and Quantum Numbersmentioning

confidence: 99%

“…After using the (m, n) system to eliminate n 1 and n 2 , the finitized character gives the fermionic representation of the usual Virasoro character in the limit N → ∞ In this section we derive the TBA equations for the (r, s) = (1, 1) boundary by solving the TBA functional equations in the scaling limit for even N. We follow closely the derivations in [20] and [24]. The derivation for other boundary conditions is similar.…”

Section: Classification: (M N) Systems and Quantum Numbersmentioning

confidence: 99%

“…By going to the critical limit t → 0, and comparing these equations with the corresponding equations in [20], one finds that C 1 = C 2 = 0. In effect we are fixing the branches of the logarithms of l j exactly as in the critical case.…”

Section: Classification: (M N) Systems and Quantum Numbersmentioning

confidence: 99%

“…This entails perturbing the analysis of O'Brien, Pearce and Warnaar [20] off criticality. To handle the problem of classification of all the excitations it is easier to introduce boundaries and to work on the cylinder even though a study of boundary properties is not our primary goal.…”

Section: Introductionmentioning

confidence: 99%

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Excited TBA equations I: Massive tricritical Ising model

2001

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We consider the massive tricritical Ising model M(4, 5) perturbed by the thermal operator ϕ 1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r, s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A 4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m, n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r, s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters χ r,s (q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II.

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“…A 2-string is a pair of zeros (u j , u The relations [20] between these numbers determining the string content take the form of an (m, n)-system [21,22] …”

Section: Classification: (M N) Systems and Quantum Numbersmentioning

confidence: 99%

Section: Classification: (M N) Systems and Quantum Numbersmentioning

confidence: 99%

Section: Classification: (M N) Systems and Quantum Numbersmentioning

confidence: 99%

Section: Classification: (M N) Systems and Quantum Numbersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Excited TBA equations I: Massive tricritical Ising model

2001

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Integrable Boundaries and Universal TBA Functional Equations

Chui

Mercat

Pearce

2002

MathPhys Odyssey 2001

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Paths, Crystals and Fermionic Formulae

Hatayama

Kuniba

Okado

et al. 2002

MathPhys Odyssey 2001

129

286

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We introduce a fermionic formula associated with any quantum affine algebra Uq(X (r) N ). Guided by the interplay between corner transfer matrix and Bethe ansatz in solvable lattice models, we study several aspects related to representation theory, most crucially, the crystal basis theory. They include one dimensional sums over both finite and semi-infinite paths, spinon character formulae, Lepowski-Primc type conjectural formula for vacuum string functions, dilogarithm identities, Q-systems and their solution by characters of various classical subalgebras and so forth. The results expand [HKOTY1] including the twisted cases and more details on inhomogeneous paths consisting of non-perfect crystals. As a most intriguing example, certain inhomogeneous one dimensional sums conjecturally give rise to branching functions of an integrable G

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Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries

Cited by 26 publications

References 31 publications

Excited TBA equations I: Massive tricritical Ising model

Excited TBA equations I: Massive tricritical Ising model

Integrable Boundaries and Universal TBA Functional Equations

Paths, Crystals and Fermionic Formulae

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