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Q-Operators for Higher Spin Eight Vertex Models with an Even Number of Sites

Takashi Takebe

arXiv:1509.08616Letters in Mathematical PhysicsNov 21, 20153 citations

Form factors and vertex operators in the eight-vertex model at reflectionless points

Yas-Hiro Quano

素粒子論研究Jan 20, 20060 citations

Non-universal critical behaviour of a mixed-spin Ising model on the extended Kagome lattice

Jozef Strečka, Lucia Čanová

The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagomé lattice is solved by establishing a mapping correspondence with the eight-vertex model. Letting the parameter of uniaxial single-ion anisotropy tend to infinity, the model becomes exactly soluble as a free-fermion eight-vertex model. Under this restriction, the critical points are characterized by critical exponents from the standard Ising universality class. In a certain subspace of interaction parameters that corresponds to a coexistence surface between two ordered phases, the model becomes exactly soluble as a symmetric zero-field eight-vertex model. This surface is bounded by a line of bicritical points that have non-universal interaction-dependent critical exponents.The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagomé lattice is solved by establishing a mapping correspondence with the eight-vertex model. Letting the parameter of uniaxial single-ion anisotropy tend to infinity, the model becomes exactly soluble as a free-fermion eight-vertex model. Under this restriction, the critical points are characterized by critical exponents from the standard Ising universality class. In a certain subspace of interaction parameters that corresponds to a coexistence surface between two ordered phases, the model becomes exactly soluble as a symmetric zero-field eight-vertex model. This surface is bounded by a line of bicritical points that have non-universal interaction-dependent critical exponents.

arXiv:cond-mat/0507366Jul 15, 20050 citations

Non-universal critical behaviour of a mixed-spin Ising model on the extended Kagomé lattice

Jozef Strečka, Canova

The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagom é lattice is solved by establishing a mapping correspondence with the eight-vertex model.When the parameter of uniaxial single-ion anisotropy tends to infinity, the model system becomes exactly solvable as the staggered eight-vertex model satisfying the free-fermion condition.The critical points within this manifold can be characterized by critical exponents from the standard Ising universality class.The critical points within another subspace of interaction parameters, which corresponds to a coexistence surface between two ordered phases, can be approximated by corresponding results of the uniform eight-vertex model satisfying the zero-field condition.This coexistence surface is bounded by a line of bicritical points that have non-universal continuously varying critical indices.The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagom é lattice is solved by establishing a mapping correspondence with the eight-vertex model.When the parameter of uniaxial single-ion anisotropy tends to infinity, the model system becomes exactly solvable as the staggered eight-vertex model satisfying the free-fermion condition.The critical points within this manifold can be characterized by critical exponents from the standard Ising universality class.The critical points within another subspace of interaction parameters, which corresponds to a coexistence surface between two ordered phases, can be approximated by corresponding results of the uniform eight-vertex model satisfying the zero-field condition.This coexistence surface is bounded by a line of bicritical points that have non-universal continuously varying critical indices.

Condensed Matter PhysicsJan 1, 200613 citations

The 8-Vertex Model with a Special Value of the Crossing Parameter and the Related XYZ Spin Chain

Yu. G. Stroganov

Springer eBooksJan 1, 200118 citations

A new eight vertex model and higher dimensional, multiparameter generalizations

B. Abdesselam, Amitabha Chakrabarti

We study statistical models, specifically transfer matrices corresponding to a multiparameter hierarchy of braid matrices of (2n)2×(2n)2 dimensions with 2n2 free parameters (n=1,2,3,…). The simplest, 4×4 case, is treated in detail. Powerful recursion relations are constructed by explicitly giving the dependence on the spectral parameter θ of the eigenvalues of the transfer matrix at each level of coproduct sequence. A brief study of higher dimensional cases (n⩾2) is presented, pointing out features of particular interest. Spin chain Hamiltonians are also briefly presented for the hierarchy. In a long final section, basic results are recapitulated with systematic analysis of their contents. Our eight vertex 4×4 case is compared to standard six vertex and eight vertex models.We study statistical models, specifically transfer matrices corresponding to a multiparameter hierarchy of braid matrices of (2n)2×(2n)2 dimensions with 2n2 free parameters (n=1,2,3,…). The simplest, 4×4 case, is treated in detail. Powerful recursion relations are constructed by explicitly giving the dependence on the spectral parameter θ of the eigenvalues of the transfer matrix at each level of coproduct sequence. A brief study of higher dimensional cases (n⩾2) is presented, pointing out features of particular interest. Spin chain Hamiltonians are also briefly presented for the hierarchy. In a long final section, basic results are recapitulated with systematic analysis of their contents. Our eight vertex 4×4 case is compared to standard six vertex and eight vertex models.

arXiv:0801.2548Journal of Mathematical PhysicsMay 1, 20088 citations

Q-operators for higher spin eight vertex models with a rational anisotropy parameter

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