scholarly journals Solutions for correlations along the coexistence curve and at the critical point of a kagomé lattice gas with three-particle interactions

2008 ◽  
Vol 77 (1) ◽  
Author(s):  
J. H. Barry ◽  
K. A. Muttalib ◽  
T. Tanaka
Keyword(s):  
Critical Point ◽  
Lattice Gas ◽  
Coexistence Curve ◽  
Particle Interactions ◽  
Kagome Lattice ◽  
Kagomé Lattice

EXACT PHASE DIAGRAMS FOR THE CONDENSATION OF A KAGOMÉ LATTICE GAS WITH THREE-PARTICLE INTERACTIONS

1993 ◽  
Vol 07 (15) ◽  
pp. 2831-2857 ◽  
Author(s):  
J.H. BARRY ◽  
N.S. SULLIVAN
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Phase Diagrams ◽  
Lattice Gas ◽  
Coexistence Curve ◽  
Particle Interactions ◽  
Kagome Lattice ◽  
Canonical Partition Function ◽  
Kagomé Lattice ◽  
Reduced Temperature

The condensation of a two-dimensional kagomé lattice gas having purely three-particle interactions is first theoretically investigated. The Hamiltonian Hℓg=−∈3Σ<i, j, k> ninjnk, where ∈3>0 is the strength. parameter of the short-range attractive triplet interaction, the sum is taken over all elementary triangles of the kagomé lattice, and nℓ=0, 1 is an idempotent site-occupation number. The method initially involves transforming the lattice-gas model into a generalized kagomé Ising model having both pair and triplet interactions as well as a magnetic field. Since the canonical partition function of a generalized kagomé Ising model is equivalent (aside from known prefactors) to the canonical partition function of a standard honeycomb Ising model in a magnetic field, one can deduce the exact liquid-vapor phase diagrams of the triplet-interaction kagomé lattice gas from its grand canonical partition function. As results, the liquid-vapor phase boundary (reduced chemical potential μ/∈3 vs reduced temperature T/Tc) is found to be curvilinear with a positive slope, originating at zero temperature with μ/∈3=−2/3 and analytic at its terminating critical point whose coordinates are T/Tc=1, μc/∈3=−0.64469…, where ∈3/kBTc=3.96992…. The companion coexistence curve (particle number density ρ vs. reduced temperature T/Tc) exhibits an asymmetric rounded shape with a positive-slope curvilinear diameter, and the value of the critical density ρc=0.58931…. At criticality, the expression for the coexistence curve superposes a pair of branch point singularities resulting in an infinite (vertical) slope at the critical point (T/Tc=ρ/ρc=1). The case of a kagomé lattice gas having mixed attractive pair interactions and very weak repulsive triplet interactions (Axilrod-Teller) is next considered. Perturbation analyses upon exact expressions relating to the phase diagrams reveal, over chosen ranges of reduced temperatures, that the phase boundary and the diameter of the two-phase coexistence region each have a negative slope due to the repulsive three-particle interactions.

CRITICAL POINT OF THE KAGOME POTTS MODEL: A HISTOGRAM MONTE CARLO RENORMALIZATION GROUP DETERMINATION

1994 ◽  
Vol 08 (07) ◽  
pp. 455-459 ◽  
Author(s):  
CHIN-KUN HU ◽  
JAU-ANN CHEN ◽  
F. Y. WU
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Critical Point ◽  
Potts Model ◽  
Group Method ◽  
Renormalization Group Method ◽  
Kagome Lattice ◽  
Kagomé Lattice ◽  
Monte Carlo Renormalization Group

The histogram Monte Carlo renormalization group method proposed by Hu is used to determine the critical point of the q-state Potts model on the Kagome lattice. Our results are compared with the predictions of conjectures by Wu and Tsallis.

Star-Star Relation for the Potts Model

1997 ◽  
Vol 11 (01n02) ◽  
pp. 51-56 ◽  
Author(s):  
C. King ◽  
F. Y. Wu
Keyword(s):  
Critical Point ◽  
Potts Model ◽  
Unsolved Problem ◽  
Kagome Lattice ◽  
Dual Transformation ◽  
Kagomé Lattice ◽  
Special Limit ◽  
Transformation Relation

A star-star transformation is introduced for the Potts model as a generalization of the Onsager star-triangle relation. By considering a special limit of the star-star relation, we deduce a dual transformation relation for the Potts model on the 3-12 lattice. We also obtain numerical bounds on the critical point of the Potts model on the kagomé lattice, a long unsolved problem.

scholarly journals Doping Quantum Spin Liquids on the Kagome Lattice

2021 ◽  
pp. 2000126
Author(s):  
Cheng Peng ◽  
Yi‐Fan Jiang ◽  
Dong‐Ning Sheng ◽  
Hong‐Chen Jiang
Keyword(s):  
Quantum Spin ◽  
Spin Liquids ◽  
Kagome Lattice ◽  
Kagomé Lattice ◽  
Quantum Spin Liquids

On Computations of Topological Descriptors of Kagome Lattice

2021 ◽  
pp. 1-15
Author(s):  
Zahid Iqbal ◽  
Adnan Aslam ◽  
Muhammad Ishaq ◽  
Wei Gao
Keyword(s):  
Topological Descriptors ◽  
Kagome Lattice ◽  
Kagomé Lattice

scholarly journals Strain-Relief Patterns and Kagome Lattice in Self-Assembled C60 Thin Films Grown on Cd(0001)

2021 ◽  
Vol 22 (13) ◽  
pp. 6880
Author(s):  
Zilong Wang ◽  
Minlong Tao ◽  
Daxiao Yang ◽  
Zuo Li ◽  
Mingxia Shi ◽  
...  
Keyword(s):  
Thin Films ◽  
Self Assembly ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
Scanning Tunneling ◽  
Kagome Lattice ◽  
Tunneling Microscopy ◽  
Kagomé Lattice ◽  
Temperature Scanning ◽  
C60 Films

We report an ultra-high vacuum low-temperature scanning tunneling microscopy (STM) study of the C60 monolayer grown on Cd(0001). Individual C60 molecules adsorbed on Cd(0001) may exhibit a bright or dim contrast in STM images. When deposited at low temperatures close to 100 K, C60 thin films present a curved structure to release strain due to dominant molecule–substrate interactions. Moreover, edge dislocation appears when two different wavy structures encounter each other, which has seldomly been observed in molecular self-assembly. When growth temperature rose, we found two forms of symmetric kagome lattice superstructures, 2 × 2 and 4 × 4, at room temperature (RT) and 310 K, respectively. The results provide new insight into the growth behavior of C60 films.

scholarly journals Flat-Band-Enabled Triplet Excitonic Insulator in a Diatomic Kagome Lattice

2021 ◽  
Vol 126 (19) ◽  
Author(s):  
Gurjyot Sethi ◽  
Yinong Zhou ◽  
Linghan Zhu ◽  
Li Yang ◽  
Feng Liu
Keyword(s):  
Flat Band ◽  
Kagome Lattice ◽  
Kagomé Lattice ◽  
Excitonic Insulator
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