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About 9,048 papers for “triangular lattice”

Triangular-Lattice Antiferromagnet

A Monte Carlo Study, Hui Yin, Bulbul Chakraborty et al. · 1999

Using a Monte Carlo coarse-graining technique introduced by Binder et al., we have explicitly constructed the continuum field theory for the zerotemperature triangular Ising antiferromagnet. We verify the conjecture that this is a gaussian theory of the height variable in the interface representation of the spin model. We also measure the height-height correlation function and deduce the stiffness constant. In addition, we investigate the nature of defectdefect interactions at finite temperatures, and find that the two-dimensional Coulomb gas scenario holds for a low density of defects. Typeset using REVTEX 1 I.

Cited by 0

The triangular lattice.

Lin Chen (54305), Tao Li (86810), Jinfeng Liu (32678) et al. · Figshare · 2016

Cited by 0Open access

Triangular lattice exciton model

Gunlycke, Daniel, Tseng, Frank · arXiv (Cornell University) · 2015

We present a minimalistic equilateral triangular lattice model, from which we derive electron and exciton band structures for semiconducting transition-metal dichalcogenides. With explicit consideration of the exchange interaction, this model is appropriate across the spectrum from Wannier to Frenkel excitons. The single-particle contributions are obtained from a nearest-neighbor tight-binding model parameterized using the effective mass and spin-orbit coupling. The solutions to the characteristic equation, computed in direct space, are in qualitative agreement with first-principles calculations and highlight the inadequacy of the two-dimensional hydrogen model to describe the lowest-energy exciton bands. The model confirms the lack of subshell degeneracy and shows that the A-B exciton split depends on the electrostatic environment as well as the spin-orbit interaction.

Cited by 0Open access

Generalized Triangular Ising Lattice

R. G. J. Mills, C. A. Hurst · Journal of Mathematical Physics · 1969

The partition function and critical equations for the generalized triangular Ising lattice are determined in terms of weight factors associated with the decorating lattice. As an example, a lattice which incorporates the Kagome, hexagonal, triangular, and rectangular lattices is solved by the method developed.

Cited by 1

the Compressible Triangular Lattice Antiferromagnet

Hui Yin, Bulbul Chakraborty · 2000

In an effort to understand the glass transition, the kinetics of a spin model with frustration but no quenched randomness has been analyzed. The phenomenology of the spin model is similar to that of a supercooled liquid undergoing the glass transition. The slow dynamics exhibited by the spins can be associated with the presence of extended string-like structures which demarcate regions of fast spins. A thermodynamic phase transition, with the string density as the order parameter, can be related to the observed glass transition in the spin model. I.

Cited by 0

Kagome-Triangular Lattice Antiferromagnet NaBa2Mn3F11

Ishikawa, Hajime, Okubo, Tsuyoshi, Okamoto, Yoshihiko et al. · arXiv (Cornell University) · 2014

A new type of magnetically frustrated lattice is found in the layered fluoride NaBa2Mn3F11. A kagome-type array of regular triangles composed of Mn2+ ions (spin 5/2) deforms so as to generate the next-nearest-neighbor interaction J2 between three out of six spins in the hexagon of a normal kagome lattice, in addition to the nearest-neighbor interaction J1. As a function of |J2/J1|, this lattice can interconnect the kagome (J2 = 0) and the triangular (J2 = J1) lattices and thus is called the kagome-triangular (KT) lattice. Magnetic susceptibility and heat capacity measurements performed on a polycrystalline sample of NaBa2Mn3F11 show an intensive short-range antiferromagnetic correlation below 14 K probably due to the specific magnetic frustration of the KT lattice. In addition, a long-range order at 2.0 K is observed, which is significantly low compared with the antiferromagnetic Weiss temperature of 32.3 K. Theoretical considerations of Heisenberg spins in the KT lattice reveal unique non-coplanar magnetic orders in the case of ferromagnetic J1 and antiferromagnetic J2. NaBa2Mn3F11 may actually exist in this regime according to the results of our analysis based on classical Monte-Carlo simulation.

Cited by 0Open access

III. Triangular-lattice chromatic polynomial

Jesper Lykke Jacobsen, Jesús Salas, Alan D. Sokal · 2002

We study the chromatic polynomial PG(q) for m×n triangular-lattice strips of widths m ≤ 12P,9F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such strips in the Fortuin–Kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q-plane in the limit n → ∞. We recompute the limiting curve obtained by Baxter in the thermodynamic limit m,n → ∞ and find new interesting features with possible physical consequences. Finally, we analyze the isolated limiting points and their relation with the Beraha numbers. Key Words: Chromatic polynomial; chromatic root; antiferromagnetic Potts model; triangular lattice; transfer matrix; Fortuin–Kasteleyn representation; Beraha–Kahane–

Cited by 0

Finite lattice series expansions for the triangular lattice

I. G. Enting · Journal of Physics A Mathematical and General · 1980

It is shown that, on the triangular lattice, series expansions for the Ising model and related problems in lattice statistics can be obtained by combining the contributions of finite hexagonal regions. This generalises earlier results for square lattice systems.

Cited by 9

Quantum Lattice Gas Model on the Triangular Lattice

Seiji Miyashita · Japanese Journal of Applied Physics · 1987

The coexistence of the diagonal long range order and the off-diagonal long range order is discussed for a model with frustrated Interaction on the triangular lattice. Nature of order parameters are compared with those of the classical model.

Cited by 1

Bethe ansatz solution of triangular trimers on the triangular lattice

Alain Verberkmoes, Bernard Nienhuis · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2001

Recently, a model consisting of triangular trimers covering the triangular lattice was introduced and its exact free energy given. In this paper we present the complete calculation leading to this exact result. The solution involves a coordinate Bethe ansatz with two kinds of particles. It is similar to that of the square-triangle random tiling model by Widom and Kalugin. The connection of the trimer model with related solvable models is discussed.

Cited by 11Open access