Phase Separation Due to Nearest Neighbor Attractive Interactions in a Two-Dimensional Model

2003 ◽  
Vol 17 (16) ◽  
pp. 853-861 ◽  
Author(s):  
M. Shaw ◽  
W. P. Su
Keyword(s):  
Phase Separation ◽  
Long Range ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Nearest Neighbor ◽  
Square Lattice ◽  
Correlation Effects ◽  
Dimensional Model ◽  
Long Range Correlations ◽  
Half Filling

We have studied a correlated fermion model with nearest neighbor attractive interactions on a square lattice by means of quantum Monte Carlo simulation. At half-filling this model exhibits rather strong correlation effects. Charge fluctuations are suppressed and the ground state is an insulator with long-range anitferromagnetic correlations. When doped with holes this model exihibits phase separation which seems to be triggered by the antiferromagnetic long-range correlations.

LONG-RANGE ORDER FOR THE 3-STATE SQUARE LATTICE POTTS MODEL WITH ANTIFERROMAGNETIC “THE MOVE OF THE KNIGHT” INTERACTIONS

1996 ◽  
Vol 10 (15) ◽  
pp. 731-736
Author(s):  
A.V. BAKAEV ◽  
V.I. KABANOVICH
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Long Range ◽  
Potts Model ◽  
Ground State ◽  
Nearest Neighbor ◽  
Two Dimensions ◽  
Range Order ◽  
Square Lattice ◽  
Long Range Order

The 3-state square lattice Potts model with interactions of spins belonging to the different sublattices, the nearest-neighbor (NN) interaction and “the move of the knight” (MK) antiferromagnetic interactions which also couples spins on the sublattice A to spins on B, is studied by Monte Carlo simulations. It is shown that the MK-interactions stabilizes the BSS phase in two dimensions, preserving macroscopic degeneracy of the ground state. In a range of competing ferromagnetic (NN) interactions “stripes” or “double-stripes” phases are found.

The Phase Diagram of the Two-Dimensional t-J Model from High Temperature Expansions

1992 ◽  
Vol 06 (05n06) ◽  
pp. 585-585
Author(s):  
W.O. Putikka ◽  
M.U. Luchini ◽  
T.M. Rice
Keyword(s):  
Phase Diagram ◽  
Free Energy ◽  
Phase Separation ◽  
High Temperature ◽  
Quantum Monte Carlo ◽  
Helmholtz Free Energy ◽  
Continuation Methods ◽  
Square Lattice ◽  
Cluster Method ◽  
Half Filling

The phase diagram of the 2D t-J model has been investigated using high temperature expansions. Series for the Helmholtz free energy, the inverse compressibility, the chemical potential and the uniform spin susceptibility through tenth order on a square lattice have been calculated using the finite cluster method.1 The series are analytically continued beyond their radius of convergence by Padé and integral approximants. The most accurate extrapolations can be made for the Helmholtz free energy where for J/t≈0.3 and n≈0.9 we can reach T~t/5. We can test the accuracy of the continuation methods by comparing with the 1D results for the boundary of phase separation of Ogata et al.2 In 2D a region of phase separation was found at T=0 for J/t lying above a line extending from J/t=3.8 at zero filling to J/t=1.2 at half filling. No phase separation was found at very small J/t contrary to the earlier suggestion of Emery et al3 which was based on results from exact diagonalisation on 4×4 clusters but in agreement with Quantum Monte Carlo (QMC) calculations on the Hubbard model.4 For very small J/t near half filling where the Nagaoka effect is possible, we find a region of divergent uniform magnetic susceptibility at T=0. However the divergence is very weak when compared with the exponential behaviour expected from a 2D ferromagnet. This might imply a substantially reduced moment which is consistent with the recent QMC estimates of Zhang et al.5

scholarly journals Complete catalog of ground-state diagrams for the general three-state lattice-gas model with nearest-neighbor interactions on a square lattice

2019 ◽  
Vol 21 (11) ◽  
pp. 6216-6223 ◽  
Author(s):  
Daniel Silva ◽  
Per Arne Rikvold
Keyword(s):  
Phase Diagrams ◽  
Ground State ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Square Lattice ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Dimensional Parameter ◽  
State Diagrams ◽  
Solid Foundation

The fifteen topologically different zero-temperature phase diagrams in the model's full, five-dimensional parameter space provide a solid foundation for studies at finite temperatures.

GROUND STATE OF THE 2D EXTENDED HUBBARD MODEL WITH MORE THAN NEAREST-NEIGHBOR INTERACTIONS

2012 ◽  
Vol 26 (29) ◽  
pp. 1250156 ◽  
Author(s):  
S. HARIR ◽  
M. BENNAI ◽  
Y. BOUGHALEB
Keyword(s):  
Phase Diagram ◽  
Hubbard Model ◽  
Ground State ◽  
State Energy ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Extended Hubbard Model ◽  
Eigenvalues And Eigenvectors ◽  
Repulsion Energy

We investigate the ground state phase diagram of the two dimensional Extended Hubbard Model (EHM) with more than Nearest-Neighbor (NN) interactions for finite size system at low concentration. This EHM is solved analytically for finite square lattice at one-eighth filling. All eigenvalues and eigenvectors are given as a function of the on-site repulsion energy U and the off-site interaction energy Vij. The behavior of the ground state energy exhibits the emergence of phase diagram. The obtained results clearly underline that interactions exceeding NN distances in range can significantly influence the emergence of the ground state conductor–insulator transition.

scholarly journals Functional-Integral Approach to the Investigation of the Spin-Spiral Magnetic Order and Phase Separation

2012 ◽  
Vol 190 ◽  
pp. 7-10
Author(s):  
Anatoly K. Arzhnikov ◽  
A.G. Groshev
Keyword(s):  
Phase Separation ◽  
Nearest Neighbor ◽  
Single Layer ◽  
Functional Integral ◽  
Integral Approach ◽  
Unusual Behavior ◽  
Field Representation ◽  
Static Approximation ◽  
Magnetic Phases ◽  
Half Filling

We investigate a two–dimensional single-band Hubbard model with a nearest–neighbor hopping. We treat a commensurate collinear order as well as incommensurate spiral magnetic phases at a finite temperature using a Hubbard–Stratonovich transformation with a two–field representation and solve this problem in a static approximation. We argue that temperature dramatically influence the collinear and spiral magnetic phases, phase separation in the vicinity of half–filling. The results imply a possible interpretation of unusual behavior of magnetic properties of single–layer cuprates.

ENTANGLEMENT IN ONE-AND TWO-DIMENSIONAL ANDERSON MODELS WITH LONG-RANGE CORRELATED-DISORDER

2009 ◽  
Vol 07 (05) ◽  
pp. 959-968
Author(s):  
Z. Z. GUO ◽  
Z. G. XUAN ◽  
Y. S. ZHANG ◽  
XIAOWEI WU
Keyword(s):  
Long Range ◽  
Ground State ◽  
Two Dimensions ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Correlation Effects ◽  
Von Neumann ◽  
Range Correlation ◽  
The Difference ◽  
Anderson Models

The ground state entanglement in one- and two-dimensional Anderson models are studied with consideration of the long-range correlation effects and using the measures of concurrence and von Neumann entropy. We compare the effects of the long-range power-law correlation for the on-site energies on entanglement with the uncorrelated cases. We demonstrate the existence of the band structure of the entanglement. The intraband and interband jumping phenomena of the entanglement are also reported and explained to as the localization-delocalization transition of the system. We also demonstrated the difference between the results of one- and two-dimensions. Our results show that the correlation of the on-site energies increases the entanglement.

NUMERICAL SIMULATION OF THE 1D AND 2D HUBBARD MODELS: FERMI LIQUID BEHAVIOR AND ITS BREAKDOWN

1988 ◽  
Vol 02 (05) ◽  
pp. 993-1003 ◽  
Author(s):  
S. Sorella ◽  
E. Tosatti ◽  
S. Baroni ◽  
R. Car ◽  
M. Parrinello
Keyword(s):  
Ground State ◽  
Fermi Liquid ◽  
Finite Size ◽  
Simulation Method ◽  
Square Lattice ◽  
Antiferromagnetic Order ◽  
Hubbard Models ◽  
Clear Sign ◽  
Liquid Behavior ◽  
Half Filling

The ground state of the 1D and of the 2D (square lattice) finite-size Hubbard model is investigated for variable filling using a novel quantum simulation method. We have studied up to 256 sites for both 1D and 2D. Away from half filling the 2D antiferromagnetic order is initially destroyed, albeit without any clear sign of a Fermi liquid behaviour. A metallic jump in n(k) appears only very far from half filling. In the 1D case, by contrast, a Fermi liquid-like jump in n(k) is obtained even very close to half filling.

scholarly journals On the Validity of the Dynamical Mean-Field Approximation for Studying the Two-Dimensional Hubbard Model on a Square Lattice

2010 ◽  
Vol 2010 ◽  
pp. 1-5 ◽  
Author(s):  
A. N. Ribeiro ◽  
C. A. Macedo
Keyword(s):  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Mean Field ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Two Dimensional ◽  
Infinite Dimensions ◽  
Antiferromagnetic Correlations ◽  
Half Filling

The dynamical mean-field approximation (DMFA) becomes exact in the limit of infinite dimensions, and allows results to be obtained in a nonperturbative regime without the limitations normally found with exact diagonalization (ED) and quantum Monte Carlo (QMC) methods. In this paper, we investigate the applicability of the method to lattices with small coordination number in special situations. Specifically we use this approximation to study the two-dimensional (2D) Hubbard model on a square lattice far from half filling. In this situation, we calculate the specific heat and find that when the filling decreases, that is, antiferromagnetic correlations become less important, the agreement between DMFA and QMC results increases. Our results show that the DMFA can be a valuable technique for studying the thermodynamic properties of the Hubbard model also on a square lattice, but within a parameter range in which the antiferromagnetic correlations are not important.

scholarly journals Phase transition and monopole densities in a nearest neighbor two-dimensional spin ice model

2017 ◽  
Vol 31 (31) ◽  
pp. 1750237
Author(s):  
C. W. Morais ◽  
D. N. De Freitas ◽  
A. L. Mota ◽  
E. C. Bastone
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Ground State ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
Dipolar Interaction ◽  
Effective Model ◽  
Two Dimensional ◽  
Spin Ice ◽  
Ice Model

In this work, we show that, due to the alternating orientation of the spins in the ground state of the artificial square spin ice, the influence of a set of spins at a certain distance of a reference spin decreases faster than the expected result for the long range dipolar interaction, justifying the use of the nearest neighbor two-dimensional square spin ice model as an effective model. Using an extension of the model presented in Y. L. Xie et al., Sci. Rep. 5, 15875 (2015), considering the influence of the eight nearest neighbors of each spin on the lattice, we analyze the thermodynamics of the model and study the dependence of monopoles and string densities as a function of the temperature.

Sign in / Sign up

Export Citation Format

Share Document