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Renormalization group flow of the two-dimensional Ising model at T<Tc

Antonio González-arroyo A, Jesús Salas

Physics Letters BJun 1, 19916 citations

Renormalization and scaling of a two-dimensional Ising system in a transverse field at Tc>0

Stella, A.L., Toigo, F.

A quantum generalization of the Niemeijer and van Leeuwen (N-vL) renormalization group transformation is constructed which allows to study the critical properties (at Tc>0) of a two-dimensional Ising system with a transverse field on a triangular lattice. Explicit calculations are performed in a second order cumulant expansion. Only one fixed point is found corresponding to the same Ising-like hamiltonian given by N-vl. The linearized transformation has a zero eigenvalue associated with Γ, the transverse field strength. The critical properties of the system are briefly discussed; in particular we show that the singular behaviour of the transverse susceptibility at Γ = 0, which turns out to be of the same kind as that of the energy density, is explained by the existence of such a zero eigenvalue. Our arguments suggest a natural extension of this result to three dimensions.A quantum generalization of the Niemeijer and van Leeuwen (N-vL) renormalization group transformation is constructed which allows to study the critical properties (at Tc>0) of a two-dimensional Ising system with a transverse field on a triangular lattice. Explicit calculations are performed in a second order cumulant expansion. Only one fixed point is found corresponding to the same Ising-like hamiltonian given by N-vl. The linearized transformation has a zero eigenvalue associated with Γ, the transverse field strength. The critical properties of the system are briefly discussed; in particular we show that the singular behaviour of the transverse susceptibility at Γ = 0, which turns out to be of the same kind as that of the energy density, is explained by the existence of such a zero eigenvalue. Our arguments suggest a natural extension of this result to three dimensions.

Jan 1, 19770 citations

Real-space renormalization group for the transverse-field Ising model in two and three dimensions

涼二宮崎, Ryoji Miyazaki, 秀稔西森 +2 more

May 1, 20110 citations

Ising model with a transverse field in two dimensions: Phase diagram and critical properties from a real-space renormalization group

Zvi Friedman

Critical indices, the critical line, and the crossover scaling function for the free energy are calculated for the two-dimensional Ising model with a transverse field using a quantum-mechanical version of the real-space renormalization group. The critical behavior as function of the transverse field at a small finite temperature changes from that of a three-dimensional to that of a two-dimensional Ising behavior, as the critical line is approached.

Physical review. B, Condensed matterFeb 1, 197824 citations

Finite-temperature scaling at the quantum critical point of the Ising chain in a transverse field

M. Hälg, D. Hüvonen, T. Guidi +4 more

Bulletin of the American Physical SocietyMar 6, 20150 citations

Critical behavior of the two-dimensional Ising model in a transverse field: A density-matrix renormalization calculation

M. S. L. du Croo de Jongh, J. M. J. van Leeuwen

We have adjusted the density-matrix renormalization method to handle two-dimensional systems of limited width. The key ingredient for this extension is the incorporation of symmetries in the method. The advantage of our approach is that we can force certain symmetry properties to the resulting ground-state wave function. Combining the results obtained for system sizes up to $30\ifmmode\times\else\texttimes\fi{}6$ and finite-size scaling, we derive the phase-transition point and the critical exponent for the gap in the Ising model in a transverse field on a two-dimensional square lattice.We have adjusted the density-matrix renormalization method to handle two-dimensional systems of limited width. The key ingredient for this extension is the incorporation of symmetries in the method. The advantage of our approach is that we can force certain symmetry properties to the resulting ground-state wave function. Combining the results obtained for system sizes up to $30\ifmmode\times\else\texttimes\fi{}6$ and finite-size scaling, we derive the phase-transition point and the critical exponent for the gap in the Ising model in a transverse field on a two-dimensional square lattice.

arXiv:cond-mat/9709103Physical review. B, Condensed matterApr 1, 199865 citations

Renormalization and scaling of a two-dimensional Ising system in a transverse field at Tc>0

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