In this paper, we consider the unitary critical restricted-solid-on-solid (RSOS) lattice $\mathcal{M}(5,6)$ model with integrable boundary conditions. We introduce its commuting double row transfer matrix satisfying the universal functional relations, and we use it in order to study the analytic structure of the transfer matrix eigenvalues and plot representative zero configurations of sample eigenvalues of the transfer matrix. We finally conclude with a comparative analysis with the critical and tricritical Ising models with integrable boundary conditions.In this paper, we consider the unitary critical restricted-solid-on-solid (RSOS) lattice $\mathcal{M}(5,6)$ model with integrable boundary conditions. We introduce its commuting double row transfer matrix satisfying the universal functional relations, and we use it in order to study the analytic structure of the transfer matrix eigenvalues and plot representative zero configurations of sample eigenvalues of the transfer matrix. We finally conclude with a comparative analysis with the critical and tricritical Ising models with integrable boundary conditions.

arXiv:1805.05949International Journal of Applied Mathematics & Statistics/International journal of applied mathematics and statisticsMay 15, 20181 citation

Ising model with long-range interaction

S. H. Florez, M. Roldán

Revista Colombiana de FísicaJan 1, 19970 citations

Boundary Quantum Field Theories with Infinite Resonance States

Mosconi, P, Mussardo, G, Riva, V

We extend a recent work by Mussardo and Penati on integrable quantum field theories with a single stable particle and an infinite number of unstable resonance states, including the presence of a boundary. The corresponding scattering and reflection amplitudes are expressed in terms of Jacobian elliptic functions, and generalize the ones of the massive thermal Ising model and of the Sinh-Gordon model. In the case of the generalized Ising model we explicitly study the ground state energy and the one-point function of the thermal operator in the short-distance limit, finding an oscillating behaviour related to the fact that the infinite series of boundary resonances does not decouple from the theory even at very short-distance scales. The analysis of the generalized Sinh-Gordon model with boundary reveals an interesting constraint on the analytic structure of the reflection amplitude. The roaming limit procedure which leads to the Ising model, in fact, can be consistently performed only if we admit that the nature of the bulk spectrum uniquely fixes the one of resonance states on the boundary.We extend a recent work by Mussardo and Penati on integrable quantum field theories with a single stable particle and an infinite number of unstable resonance states, including the presence of a boundary. The corresponding scattering and reflection amplitudes are expressed in terms of Jacobian elliptic functions, and generalize the ones of the massive thermal Ising model and of the Sinh-Gordon model. In the case of the generalized Ising model we explicitly study the ground state energy and the one-point function of the thermal operator in the short-distance limit, finding an oscillating behaviour related to the fact that the infinite series of boundary resonances does not decouple from the theory even at very short-distance scales. The analysis of the generalized Sinh-Gordon model with boundary reveals an interesting constraint on the analytic structure of the reflection amplitude. The roaming limit procedure which leads to the Ising model, in fact, can be consistently performed only if we admit that the nature of the bulk spectrum uniquely fixes the one of resonance states on the boundary.

Jul 10, 20019 citations

Solutions of the Ising model

Jaka Strajn

Jun 15, 20220 citations

Dynamics of the Ising model

Huey Wen Huang

Physics Letters AJul 1, 19744 citations

Boundary Field Theory

Giuseppe Mussardo

Abstract Quantum field theory with boundaries is a very rich subject both from purely theoretical point of view or applicative aims. Chapter 21 presents the basis results relative to critical systems and massive integrable field theories. It covers stress-energy tensor in boundary conformal field theories and integrable deformations of these theories (including the single Virasoro algebra), reflection amplitudes, conformal boundary operators and states (including the Hilbert space and Ishibashi state), non-renormalizable states of the Hilbert space, operator product expansion involving a boundary operator, massive integrable boundary field theory, the massive boundary Ising model, boundary magnetic fields and correlation functions.Abstract Quantum field theory with boundaries is a very rich subject both from purely theoretical point of view or applicative aims. Chapter 21 presents the basis results relative to critical systems and massive integrable field theories. It covers stress-energy tensor in boundary conformal field theories and integrable deformations of these theories (including the single Virasoro algebra), reflection amplitudes, conformal boundary operators and states (including the Hilbert space and Ishibashi state), non-renormalizable states of the Hilbert space, operator product expansion involving a boundary operator, massive integrable boundary field theory, the massive boundary Ising model, boundary magnetic fields and correlation functions.

Mar 26, 20201 citation

In this paper, we consider the unitary critical restricted-solid-on-solid (RSOS) lattice

\mathcal{M}(5,6)

model with integrable boundary conditions. We introduce its commuting double row transfer matrix satisfying the universal functional relations, and we use it in order to study the analytic structure of the transfer matrix eigenvalues and plot representative zero configurations of sample eigenvalues of the transfer matrix. We finally conclude with a comparative analysis with the critical and tricritical Ising models with integrable boundary conditions.