Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities

DOI10.1007/BF01010471zbMath0625.10010OpenAlexW1980139645MaRDI QIDQ579294

Publication date: 1985

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01010471

zbMATH Keywords

elliptic functions eight-vertex solid-on-solid (SOS) model generalizations of the Rogers-Ramanujan identities hard-hexagon model two- dimensional lattice models

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Elementary theory of partitions (11P81)

Related Items (51)

A BURGE TREE OF VIRASORO-TYPE POLYNOMIAL IDENTITIES ⋮ Rogers-Ramanujan identities for partitions with n copies of n ⋮ The emerging role of number theory in exactly solvable models in lattice statistical mechanics ⋮ Central charge and the Andrews–Bailey construction ⋮ Finite-volume spectra of the Lee-Yang model ⋮ Lattice models, deformed Virasoro algebra and reduction equation ⋮ Lattice gas generalization of the hard hexagon model. I: Star-triangle relation and local densities ⋮ Partitions with prescribed hook differences ⋮ Bailey flows and Bose-Fermi identities for the conformal coset models $(A^{(1)}_1)_N\times (A^{(1)}_1)_{N^\prime}/ (A^{(1)}_1)_{N+N^\prime{}}$ ⋮ Ghost series and a motivated proof of the Andrews-Bressoud identities ⋮ Multinomials and polynomial bosonic forms for the branching functions of the $\widehat{su}(2)_{M}\times \widehat{su}(2)_{N}/\widehat{su}(2)_{M+N}$ conformal coset models ⋮ Continued fractions and fermionic representations for characters of $M(p,p')$ minimal models ⋮ Expectation values of local fields in the Bullough-Dodd model and integrable perturbed conformal field theories ⋮ A quartet of fermionic expressions for $M(k,2k\pm 1)$ Virasoro characters via half-lattice paths ⋮ The perturbations $\phi_{2,1}$ and $\phi_{1,5}$ of the minimal models $M(p,p^\prime$) and the trinomial analogue of Bailey's lemma ⋮ Critical site percolation on the triangular lattice: from integrability to conformal partition functions ⋮ Critical RSOS and minimal models: fermionic paths, Virasoro algebra and fields ⋮ A bijection between paths for the ${\mathcal M}(p, 2p + 1)$ minimal model Virasoro characters ⋮ Off-critical local height probabilities on a plane and critical partition functions on a cylinder ⋮ Path representation of $\hat{su}(2)_k$ states. I: Operators and particles for $k=1,2$ ⋮ Coset graphs in bulk and boundary logarithmic minimal models ⋮ Path representation of $\hat{su}(2)_k$ states. II: Operator construction of the fermionic character and spin-$\frac{1}{2}$-RSOS factorization ⋮ Exact solution of cyclic solid-on-solid lattice models ⋮ The critical boundary RSOS $\mathcal M (3,5)$ model ⋮ Fusion hierarchies, T-systems and Y-systems for the dilute $\boldsymbol{A_2^{(2)}}$ loop models ⋮ On the elliptic 𝔤𝔩2 solid-on-solid model: Functional relations and determinants ⋮ Off-critical logarithmic minimal models ⋮ Fusion hierarchies,T-systems, andY-systems of logarithmic minimal models ⋮ Kac boundary conditions of the logarithmic minimal models ⋮ RSOS quantum chains associated with off-critical minimal models and ${\boldsymbol{\mathbb{Z}}}_{{\mbox{\tssabi n}}}$ parafermions ⋮ Logarithmic minimal models with Robin boundary conditions ⋮ One-dimensional sums and finitized characters of 2 × 2 fused RSOS models ⋮ Scattering matrix for current-current deformations of the $(2,2s+1)$ RSOS models ⋮ Generalizations of the Andrews-Bressoud identities for the $N = 1$ superconformal model $SM(2, 4\nu )$ ⋮ Boundary conditions in rational conformal field theories. ⋮ Paths and partitions: Combinatorial descriptions of the parafermionic states ⋮ Fermi-gas interpretation of the RSOS path representation of the superconformal unitary minimal models ⋮ Boundary algebras and Kac modules for logarithmic minimal models ⋮ q -Trinomial identities ⋮ Bilateral Bailey lemma and Rogers-Ramanujan identities ⋮ Logarithmic minimal models ⋮ Geometric exponents, SLE and logarithmic minimal models ⋮ The space of local operators in perturbed conformal field theories ⋮ Boundary conditions in rational conformal field theories ⋮ A new path description for the {\cal M} (k+1,2k+3) models and the dual {\cal Z}_k graded parafermions ⋮ Critical behaviour of the dilute $O(n)$, Izergin-Korepin and dilute $A_L$ face models: Bulk properties ⋮ Fusion hierarchies,T-systems andY-systems for the ${A_2^{(1)}}$ models ⋮ Yang–Baxter integrable dimers on a strip ⋮ A monomial basis for the Virasoro minimal series $M(p,p')$: the case $1<p'/p<2$ ⋮ Solvable models in statistical mechanics, from Onsager onward. ⋮ Polynomial identities, indices, and duality for the $N=1$ superconformal model $SM(2,4\nu)$.

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