A MEAN FIELD APPROACH TO THE COLORED HUBBARD MODEL

2001 ◽  
Vol 16 (11) ◽  
pp. 2003-2008
Author(s):  
TOBIAS BAIER ◽  
EIKE BICK
Keyword(s):  
Mean Field ◽  
Scalar Fields ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Antiferromagnetic Order ◽  
Expectation Values ◽  
Field Approach ◽  
Antiferromagnetic Ordering ◽  
Measured Phase Diagram

By subdividing a 2d square lattice into plaquettes containing 4 lattice sites each, the Hubbard Hamiltonian is reformulated in terms of different "colored" fermion species. This makes it possible to describe e.g. antiferromagnetic order or d-wave superconductivity in terms of expectation values of composite scalar fields. A suitable mean field approximation indeed reproduces qualitatively the measured phase diagram and shows a competition between phases with antiferromagnetic ordering and dx2-y2-superconductivity at low temperatures.

scholarly journals Several Physical Properties of Two Interacting Complex Scalar Fields at Finite Density

2011 ◽  
Vol 21 (1) ◽  
pp. 1
Author(s):  
Tran Huu Phat ◽  
Phan Thi Duyen
Keyword(s):  
Mean Field ◽  
Scalar Fields ◽  
Meissner Effect ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Goldstone Theorem ◽  
Complex Scalar ◽  
Finite Density ◽  
Chemical Potentials ◽  
The Mean

The two interacting complex scalar fields at finite density is considered in the mean field approximation. It is shown that although the symmetry is spontaneously broken for the chemical potentials bigger than the meson masses in vacuum, but the Goldstone theorem is not preserved in broken phase. Then two mesons are condensed and their condensates turn out to be two-gap superconductor which is signaled by the appearance of the Meissner effect as well as the Abrikosov and non-Abrikosov vortices. Finally, there exhibits domain wall which is the plane, where two condensates flowing in opposite directions collide and generate two types of vortices with cores in the wall.

scholarly journals Failure of mean-field approximation in weakly coupled dilaton gravity

2018 ◽  
Vol 191 ◽  
pp. 07004
Author(s):  
Maxim Fitkevich
Keyword(s):  
Black Hole ◽  
Mean Field ◽  
Direct Calculation ◽  
Scalar Fields ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Massless Scalar ◽  
Dilaton Gravity ◽  
Black Hole Evaporation ◽  
Weakly Coupled

We investigate black hole evaporation in a weakly coupled model of two-dimensional dilaton gravity paying a particular attention to the validity of the semiclassical mean-field approximation. Our model is obtained by adding a reflecting boundary to the celebrated RST model describing N gravitating massless scalar fields to one-loop level. The boundary cuts off the region of strong coupling. Although our model is explicitly weakly coupled, we find that the mean field approximation inevitably fails at the end of black hole evaporation. We propose an alternative semiclassical method aiming at direct calculation of S-matrix elements and illustrate it in a simple shell model.

POSSIBLE COEXISTENCE OF ANTIFERROMAGNETISM AND SUPERCONDUCTIVITY IN THE HUBBARD MODEL

1988 ◽  
Vol 01 (09n10) ◽  
pp. 341-347 ◽  
Author(s):  
SHEN JUE-LIAN ◽  
SU ZHAO-BIN ◽  
DONG JIN-MING ◽  
YU LU
Keyword(s):  
Hubbard Model ◽  
High Temperature Superconductivity ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Antiferromagnetic Order ◽  
Effective Hamiltonian ◽  
Hamiltonian Approach ◽  
Theoretical Approaches ◽  
The Mean

The Hubbard model in the nearly half-filled case was studied in the mean field approximation using the effective Hamiltonian approach. Both antiferromagnetic order parameter and condensation of singlet pairs were considered. In certain parameter range the coexistence of antiferromagnetism and superconductivity is energetically favorable. Relations to the high temperature superconductivity and other theoretical approaches are also discussed.

scholarly journals DYNAMICAL MODEL FOR VIRUS SPREAD

Fractals ◽  
1996 ◽  
Vol 04 (02) ◽  
pp. 113-122 ◽  
Author(s):  
G. CAMELO-NETO ◽  
S. COUTINHO
Keyword(s):  
Steady State ◽  
Mean Field ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Model Parameters ◽  
Viral Spread ◽  
Infected Cells ◽  
The Mean ◽  
Density Population

The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest like cellular automaton model with two distinct populations of cells (permissive and resistant ones) and studied in the framework of the mean field approximation. Stochastic dynamical ingredients are introduced into this model to mimic cells regeneration (with probability p) and to consider infection processes by other means than contiguity (with probability f). Simulations are carried out on a L×L square lattice taking into consideration the eighth first neighbors. The mean density population of infected cells (Di) is measured as a function of the regeneration probability p, and analyzed for small values of the ratio f/p and for distinct degrees of cell resistance. The results obtained by a mean field like approach recovers the simulations results. The role of the resistant parameter R (R≥2) on the steady state properties, is investigated and discussed in comparison with the R=1 monocell case which corresponds to the self organized critical forest model. The fractal dimension of the dead cells ulcers contours was also estimated and analyzed as a function of the model parameters.

scholarly journals Fixation time in evolutionary graphs: a mean field approach

2018 ◽  
Author(s):  
Mahdi Hajihashemi ◽  
Keivan Aghababaei Samani
Keyword(s):  
Analytical Method ◽  
Transition Matrix ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Fixation Time ◽  
Field Approach ◽  
Moran Process ◽  
Structured Population ◽  
Population Structures

A novel analytical method is proposed for calculation of average fixation and extinction times of mutants in a general structured population of two types of species. The method is based on Markov chains and uses a mean field approximation to calculate the corresponding transition matrix. Analytical results are compared with the results of simulation of the Moran process on a number of population structures.

scholarly journals Stochastic Spatial Model of Producer-Consumer Systems on the Lattice

2013 ◽  
Vol 45 (4) ◽  
pp. 1157-1181 ◽  
Author(s):  
N. Lanchier
Keyword(s):  
Spatial Model ◽  
Initial Density ◽  
Mean Field ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Ecological Communities ◽  
Parameter Region ◽  
Dominant Type ◽  
The Individual

The objective of this paper is to give a rigorous analysis of a stochastic spatial model of producer-consumer systems that has been recently introduced by Kang and the author to understand the role of space in ecological communities in which individuals compete for resources. Each point of the square lattice is occupied by an individual which is characterized by one of two possible types, and updates its type in continuous time at rate 1. Each individual being thought of as a producer and consumer of resources, the new type at each update is chosen at random from a certain interaction neighborhood according to probabilities proportional to the ability of the neighbors to consume the resource produced by the individual to be updated. In addition to giving a complete qualitative picture of the phase diagram of the spatial model, our results indicate that the nonspatial deterministic mean-field approximation of the stochastic process fails to describe the behavior of the system in the presence of local interactions. In particular, we prove that, in the parameter region where the nonspatial model displays bistability, there is a dominant type that wins regardless of its initial density in the spatial model, and that the inclusion of space also translates into a significant reduction of the parameter region where both types coexist.

scholarly journals MEAN FIELD APPROACH TO THE GIANT WORMHOLE PROBLEM

1994 ◽  
Vol 03 (02) ◽  
pp. 421-430
Author(s):  
A. GAMBA ◽  
I. KOLOKOLOV ◽  
M. MARTELLINI
Keyword(s):  
Free Energy ◽  
Probability Density ◽  
Time Distribution ◽  
Mean Field ◽  
Field Approximation ◽  
Space Time ◽  
Mean Field Approximation ◽  
Field Approach

We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.

scholarly journals Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott–Antonsen theory

2020 ◽  
Vol 378 (2171) ◽  
pp. 20190259 ◽  
Author(s):  
Irina V. Tyulkina ◽  
Denis S. Goldobin ◽  
Lyudmila S. Klimenko ◽  
Igor S. Poperechny ◽  
Yuriy L. Raikher
Keyword(s):  
Magnetic Moments ◽  
Mean Field ◽  
Ferromagnetic State ◽  
Dipole Interaction ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Two Dimensional ◽  
Stripe Structure ◽  
First Order Phase

The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in two-dimensional XY arrays is addressed. The system is modelled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole–dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking T b temperature is lower than that ( T af ) of the AF transition. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean-field approximation. With the technique of a generalized Ott–Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the AF order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first-order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented. This article is part of the theme issue ‘Patterns in soft and biological matters’.

scholarly journals Comparison of several tetrahedra-based lattices

2001 ◽  
Vol 79 (11-12) ◽  
pp. 1353-1357 ◽  
Author(s):  
M Elhajal ◽  
B Canals ◽  
C Lacroix
Keyword(s):  
Energy Spectrum ◽  
Mean Field ◽  
Field Approximation ◽  
Unit Cell ◽  
Low Energy ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Effective Hamiltonian ◽  
Tetrahedral Unit

A comparison of the quantum Heisenberg anti-ferromagnetic model on the pyrochlore lattice, the checkerboard lattice, and the square lattice with crossing interactions is performed. The three lattices are constructed with the same tetrahedral unit cell and this property is used to describe the low-energy spectrum by means of an effective Hamiltonian restricted to the singlet sector. We analyze the structure of the effective Hamiltonian and solve it within a mean-field approximation for the three lattices. PACS No.: 75.10Jm

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.

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