Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Modern Physics Letters B

A UNIFIED RENORMALIZATION GROUP STUDY OF THE 1D ISING MODEL WITH TRANSVERSE FIELD

C. Y. Pan, H. Q. Lin

Published Jan 20, 1995• 0 citations
Publisher

Abstract

By applying a unified real space renormalization group (URG) mapping method, we study the one-dimensional spin-1/2 Ising model with a transverse field (ITF). Unlike the other real space renormalization group methods, the URG method describes the properties of the model at both zero and finite temperatures in a unified way. The results obtained are in good agreement with that obtained by other methods. Application of the URG method to other quantum spin systems is discussed.

DOI
10.1142/s0217984995000115

Related papers

Zero-temperature renormalization-group method for quantum systems. III. Ising model in a transverse field in two dimensions

K. A. Penson, Rémi Jullien, Pierre M. Pfeuty

A newly developed zero-temperature real-space renormalization-group method is applied to the quantum Ising model with a transverse field on different two-dimensional lattices: hexagonal, triangular, and quadratic. The order parameter, spin-spin correlation functions, the critical fields, and the critical exponents describing the low-field-large-field transition are calculated. The influence of size and shape of the spin blocks used in the iterative process is discussed. The results for triangular and hexagonal lattices are new; for the quadratic lattice the calculations show an encouraging agreement with previous series-expansion results. The expected equivalence to the critical behavior of the three-dimensional Ising model is discussed: A reasonable agreement is obtained for the hexagonal lattice.

Physical review. B, Condensed matter•May 1, 1979•61 citations

Zero-temperature renormalization-group method for quantum systems. II. Isotropic X−Y model in a transverse field in one dimension

Rémi Jullien, Pierre M. Pfeuty

A zero-temperature real-space renormalization-group method is applied to the one-dimensional quantum spin-\textonehalf{} isotropic $X\ensuremath{-}Y$ model in a transverse field. A line of unstable fixed points is found and is attributed to the oscillatory behavior of the correlation functions. Magnetization components and critical indices are in good agreement with the exact results. The behavior of the $\mathrm{xx}$ correlation function is studied near the critical field.

Physical review. B, Condensed matter•May 1, 1979•39 citations

Zero-temperature renormalization method for quantum systems. I. Ising model in a transverse field in one dimension

Rémi Jullien, Pierre M. Pfeuty, J. N. Fields +1 more

A zero-temperature real-space renormalization-group method is presented and applied to the quantum Ising model with a transverse field in one dimension. The transition between the low-field and high-field regimes is studied. Magnetization components, spin correlation functions, and critical exponents are derived and checked against the exact results. It is shown that increasing the size of the blocks in the iterative procedure yields more accurate results, especially for the critical "magnetic" exponents near the transition.

Physical review. B, Condensed matter•Oct 1, 1978•143 citations

Real Space Renormalization Group Methods and Quantum Groups

Miguel Angel Martin-Delgado, Germán Sierra

We apply real space renormalization group (RG) methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field (ITF) defined in an open chain with appropriate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearance of a quantum group anomalous term which vanishes in the classical case. We obtain correctly the line of critical XXZ models. In the ITF model the RG flow coincides with the tensor product decomposition of cyclic irreducible representations of ${\mathrm{SU}}_{q}\left(2\right)$ with ${q}^{4}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$.

arXiv:cond-mat/9507115•Physical Review Letters•Feb 12, 1996•41 citations

Renormalization-group transformation for quantum lattice systems at zero temperature

J. E. Hirsch, Gene F. Mazenko

We propose a new renormalization-group (RG) method applicable to quantum systems defined on a lattice at zero temperature. We apply our method to the one-dimensional Ising model in a transverse field and the two-dimensional triangular Ising model in a transverse field. In both cases, a nontrivial fixed point of our RG transformation is found. Critical exponents are calculated and compared with exact and previous RG results.

Physical review. B, Condensed matter•Mar 1, 1979•51 citations

Real-space renormalization-group method for quantum systems : Yang-Lee edge singularity

Katarina Uzelac, Rémi Jullien, Pierre M. Pfeuty +1 more

A T=0 real-space renormalization-group method is presented and applied to the quantum 1D transverse field Ising model in the presence of a longitudinal field. This is an indirect way to study the equation of state of the equivalent 2D classical Ising model at finite temperature. When the longitudinal field is purely imaginary we obtain a new critical behavior which is related to the Yang-Lee edge singularity of the corresponding classical model. We extract the edge exponent σ in agreement with previous series expansion estimates.

Journal of Applied Physics•Nov 1, 1979•1 citation
By applying a unified real space renormalization group (URG) mapping method, we study the one-dimensional spin-1/2 Ising model with a transverse field (ITF). Unlike the other real space renormalization group methods, the URG method describes the properties of the model at both zero and finite temperatures in a unified way. The results obtained are in good agreement with that obtained by other methods. Application of the URG method to other quantum spin systems is discussed.
A newly developed zero-temperature real-space renormalization-group method is applied to the quantum Ising model with a transverse field on different two-dimensional lattices: hexagonal, triangular, and quadratic. The order parameter, spin-spin correlation functions, the critical fields, and the critical exponents describing the low-field-large-field transition are calculated. The influence of size and shape of the spin blocks used in the iterative process is discussed. The results for triangular and hexagonal lattices are new; for the quadratic lattice the calculations show an encouraging agreement with previous series-expansion results. The expected equivalence to the critical behavior of the three-dimensional Ising model is discussed: A reasonable agreement is obtained for the hexagonal lattice.
A zero-temperature real-space renormalization-group method is applied to the one-dimensional quantum spin-\textonehalf{} isotropic $X\ensuremath{-}Y$ model in a transverse field. A line of unstable fixed points is found and is attributed to the oscillatory behavior of the correlation functions. Magnetization components and critical indices are in good agreement with the exact results. The behavior of the xx\mathrm{xx}xx correlation function is studied near the critical field.
A zero-temperature real-space renormalization-group method is presented and applied to the quantum Ising model with a transverse field in one dimension. The transition between the low-field and high-field regimes is studied. Magnetization components, spin correlation functions, and critical exponents are derived and checked against the exact results. It is shown that increasing the size of the blocks in the iterative procedure yields more accurate results, especially for the critical "magnetic" exponents near the transition.
We apply real space renormalization group (RG) methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field (ITF) defined in an open chain with appropriate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearance of a quantum group anomalous term which vanishes in the classical case. We obtain correctly the line of critical XXZ models. In the ITF model the RG flow coincides with the tensor product decomposition of cyclic irreducible representations of SUq(2){\mathrm{SU}}_{q}\left(2\right)SUq​(2) with q4=1{q}^{4}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1q4=1.
A T=0 real-space renormalization-group method is presented and applied to the quantum 1D transverse field Ising model in the presence of a longitudinal field. This is an indirect way to study the equation of state of the equivalent 2D classical Ising model at finite temperature. When the longitudinal field is purely imaginary we obtain a new critical behavior which is related to the Yang-Lee edge singularity of the corresponding classical model. We extract the edge exponent σ in agreement with previous series expansion estimates.