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

THE PARAMAGNETIC SUSCEPTIBILITY AND CROSSOVER TRANSITION IN U=∞ HUBBARD MODEL

E. G. Goryachev, D.V. KUZNETSOV

Published May 10, 1993• 0 citations
Publisher

Abstract

Paramagnetic susceptibility χ(0, 0)=dR(H)/dH in (H→0, U=∞) Hubbard model has been calculated in the second order of a kinematic field. The final result changes cardinally the conclusion about paramagnetic’s instability which was derived from the theory of the first order in kinematic field at T=0 and ρ=1/2W.1 The obtained expression for χ(0, 0) possesses Pauli limit for n→0 with factor 2, has strong correlated enhancement (≈5 times as large) in the region of intermediate filling of the band (n≈0.5), and determines the paramagnetic-ferromagnetic transition as a crossover transition (i.e. without finite or infinite discontinuity).

DOI
10.1142/s021798499300076x

Related papers

The Spin Stiffness and the Transverse Susceptibility of the Half-Filled Hubbard Model

Zhu-Pei Shi, Rajiv R. P. Singh

The T = 0 spin stiffness ρ s and the transverse susceptibility χ ⊥ of the square lattice half-filled Hubbard model are calculated as a function of the Hubbard parameter ratio U / t by series expansions around the Ising limit. We find that the calculated spin stiffness, transverse susceptibility, and sublattice magnetization for the Hubbard model smoothly approach the Heisenberg values for large U / t . The results are compared for different U / t with RPA and other numerical studies. The uniform susceptibility data indicate a crossover around U / t ≈ 4 between weak-coupling (spin density wave) behavior at small U and strong-coupling (Heisenberg) behavior at large U .

arXiv:cond-mat/9508005•Europhysics Letters (EPL)•Aug 1, 1995•8 citations

Two-dimensional Hubbard model with strong electron repulsion

L. B. Ioffe, A. I. Larkin

The two-dimensional Hubbard model is studied in the limit u/t\ensuremath{\gg}1. It is shown that almost all phase transitions are first-order transitions with a metastable-state lifetime depending discontinuously on the external parameters. The phase transition from the ferromagnetic to the ferrimagnetic state in a strong magnetic field is an exception: It is a second-order transition in a model with a half-filled electron band and it is a weakly-first-order transition in a model with a nearly-half-filled electron band. In the latter case the superconductive state is formed.

Physical review. B, Condensed matter•Apr 1, 1988•61 citations

Antiferromagnetism and the metal-insulator transition in the infinite-dimensional Hubbard model

S. Wermbter, G. Czycholl

We study the Hubbard model in infinite dimension d= infinity within an approximation reproducing simultaneously the atomic limit and the weak-coupling limit up to second order in the interaction strength U. Depending on U we find a paramagnetic metal, a paramagnetic insulator, or an antiferromagnetic insulator. The stability of the antiferromagnetic phase is investigated by calculating the grand canonical potential. We present the phase diagram in the T-U plane and results for the magnetization m as a function of temperature T. For small values of U the antiferromagnetic phase transition is continuous, but for larger values of U the approximation yields a first-order magnetic phase transition. Results for the density of states N( epsilon ) are presented; it either exhibits one single band or an upper and a lower Hubbard band separated by the Mott gap. The upper and lower Hubbard band may exhibit additional magnetic structure, depending on the value of T and U.

Journal of Physics Condensed Matter•Sep 11, 1995•7 citations

Field-dependent dynamics in the metallic regime of the half-filled Hubbard model

D Parihari, N S Vidhyadhiraja, A Taraphder

A systematic study of the effect of magnetic field (h) on the Hubbard model has been carried out at half-filling within dynamical mean field theory. In agreement with previous studies, we find a zero temperature itinerant metamagnetic transition, reflected in the discontinuous changes in magnetization as well as in the hysteresis, from a paramagnetic (PM) metallic state to a polarized quasi-ferromagnetic (QFM) state, at intermediate and large interaction strengths (U). The jump in magnetization vanishes smoothly with decreasing interaction strength, and at a critical U, the transition becomes continuous. The region of 'coexistence' of the PM and QFM solutions in the field-U plane obtained in this study agrees quantitatively with recent numerical renormalization group calculations, thus providing an important benchmark. We highlight the changes in dynamics and quasiparticle weight across this transition. The effective mass increases sharply as the transition is approached, exhibiting a cusp-like singularity at the critical field, and decreases with field monotonically beyond the transition. We conjecture that the first order metamagnetic transition is a result of the competition between Kondo screening, that tries to quench the local moments, and Zeeman coupling, which induces polarization and hence promotes local moment formation. A comparison of our theoretical results with experiments on (3)He indicate that a theory of (3)He based on the half-filled Hubbard model places it in a regime of intermediate interaction strength.

arXiv:1006.1457•Journal of Physics Condensed Matter•Jan 19, 2011•4 citations

Ferromagnetically ordered metal in the single-band hubbard model

Akihisa Koga, Yusuke Kamogawa, Joji Nasu

We study a ferromagnetic instability in a single-band Hubbard model on the hypercubic lattice away from half filling. Using dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations based on the segment algorithm, we calculate the magnetic susceptibility in the weak and strong coupling regions systematically. We then find how ferromagnetic fluctuations are enhanced when the interaction strength and density of holes are varied. The efficiency of the double flip updates in the Monte Carlo simulations is also addressed.

arXiv:1912.05053•AIP conference proceedings•Jan 1, 2021•1 citation

Crossover relationship between the magnetic susceptibility and the correlation length

Jeffrey F. Nicoll, T. S. Chang

In the asymptotic critical region of a ferromagnetic spin system, the magnetic susceptibility χ and the correlation length ξ are related by the power law: χ∼ξ2−η, where η is the correlation function exponent. Somewhat farther from the critical point, but still within the critical region, we expect the behavior to be mean-field in character: χ∼ξ2. We give an exact relationship between χ and ξ in terms of a differential renormalization group approach. The leading behavior in the disordered phase is explicitly calculated for the n-component Wilson-Fisher model to O(ε2), ε≡4−d. The result includes both limiting power laws in a smooth crossover function. For the Ising case, n=1, the relationship is extended to the entire critical region, including the ordered phase. In this case, even in the asymptotic limit, the susceptibility differs from ξ2−η by a factor which depends on the magnetization M. This function is calculated to leading order and correctly gives the associated amplitude ratios to O(ε). Applications to the general p-point vertex function are discussed.

Journal of Applied Physics•Mar 1, 1979•1 citation
Paramagnetic susceptibility χ(0, 0)=dR(H)/dH in (H→0, U=∞) Hubbard model has been calculated in the second order of a kinematic field. The final result changes cardinally the conclusion about paramagnetic’s instability which was derived from the theory of the first order in kinematic field at T=0 and ρ=1/2W.1 The obtained expression for χ(0, 0) possesses Pauli limit for n→0 with factor 2, has strong correlated enhancement (≈5 times as large) in the region of intermediate filling of the band (n≈0.5), and determines the paramagnetic-ferromagnetic transition as a crossover transition (i.e. without finite or infinite discontinuity).
The T = 0 spin stiffness ρ s and the transverse susceptibility χ ⊥ of the square lattice half-filled Hubbard model are calculated as a function of the Hubbard parameter ratio U / t by series expansions around the Ising limit. We find that the calculated spin stiffness, transverse susceptibility, and sublattice magnetization for the Hubbard model smoothly approach the Heisenberg values for large U / t . The results are compared for different U / t with RPA and other numerical studies. The uniform susceptibility data indicate a crossover around U / t ≈ 4 between weak-coupling (spin density wave) behavior at small U and strong-coupling (Heisenberg) behavior at large U .
The two-dimensional Hubbard model is studied in the limit u/t\ensuremath{\gg}1. It is shown that almost all phase transitions are first-order transitions with a metastable-state lifetime depending discontinuously on the external parameters. The phase transition from the ferromagnetic to the ferrimagnetic state in a strong magnetic field is an exception: It is a second-order transition in a model with a half-filled electron band and it is a weakly-first-order transition in a model with a nearly-half-filled electron band. In the latter case the superconductive state is formed.
We study the Hubbard model in infinite dimension d= infinity within an approximation reproducing simultaneously the atomic limit and the weak-coupling limit up to second order in the interaction strength U. Depending on U we find a paramagnetic metal, a paramagnetic insulator, or an antiferromagnetic insulator. The stability of the antiferromagnetic phase is investigated by calculating the grand canonical potential. We present the phase diagram in the T-U plane and results for the magnetization m as a function of temperature T. For small values of U the antiferromagnetic phase transition is continuous, but for larger values of U the approximation yields a first-order magnetic phase transition. Results for the density of states N( epsilon ) are presented; it either exhibits one single band or an upper and a lower Hubbard band separated by the Mott gap. The upper and lower Hubbard band may exhibit additional magnetic structure, depending on the value of T and U.
A systematic study of the effect of magnetic field (h) on the Hubbard model has been carried out at half-filling within dynamical mean field theory. In agreement with previous studies, we find a zero temperature itinerant metamagnetic transition, reflected in the discontinuous changes in magnetization as well as in the hysteresis, from a paramagnetic (PM) metallic state to a polarized quasi-ferromagnetic (QFM) state, at intermediate and large interaction strengths (U). The jump in magnetization vanishes smoothly with decreasing interaction strength, and at a critical U, the transition becomes continuous. The region of 'coexistence' of the PM and QFM solutions in the field-U plane obtained in this study agrees quantitatively with recent numerical renormalization group calculations, thus providing an important benchmark. We highlight the changes in dynamics and quasiparticle weight across this transition. The effective mass increases sharply as the transition is approached, exhibiting a cusp-like singularity at the critical field, and decreases with field monotonically beyond the transition. We conjecture that the first order metamagnetic transition is a result of the competition between Kondo screening, that tries to quench the local moments, and Zeeman coupling, which induces polarization and hence promotes local moment formation. A comparison of our theoretical results with experiments on (3)He indicate that a theory of (3)He based on the half-filled Hubbard model places it in a regime of intermediate interaction strength.
We study a ferromagnetic instability in a single-band Hubbard model on the hypercubic lattice away from half filling. Using dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations based on the segment algorithm, we calculate the magnetic susceptibility in the weak and strong coupling regions systematically. We then find how ferromagnetic fluctuations are enhanced when the interaction strength and density of holes are varied. The efficiency of the double flip updates in the Monte Carlo simulations is also addressed.
In the asymptotic critical region of a ferromagnetic spin system, the magnetic susceptibility χ and the correlation length ξ are related by the power law: χ∼ξ2−η, where η is the correlation function exponent. Somewhat farther from the critical point, but still within the critical region, we expect the behavior to be mean-field in character: χ∼ξ2. We give an exact relationship between χ and ξ in terms of a differential renormalization group approach. The leading behavior in the disordered phase is explicitly calculated for the n-component Wilson-Fisher model to O(ε2), ε≡4−d. The result includes both limiting power laws in a smooth crossover function. For the Ising case, n=1, the relationship is extended to the entire critical region, including the ordered phase. In this case, even in the asymptotic limit, the susceptibility differs from ξ2−η by a factor which depends on the magnetization M. This function is calculated to leading order and correctly gives the associated amplitude ratios to O(ε). Applications to the general p-point vertex function are discussed.