scholarly journals Spin wave theory of spin-1/2 XY model with ring exchange on a triangular lattice

2013 ◽  
Vol 91 (7) ◽  
pp. 542-547 ◽  
Author(s):  
Solomon A. Owerre
Keyword(s):  
Phase Transition ◽  
Spin Wave ◽  
Triangular Lattice ◽  
Finite Temperature ◽  
Wave Theory ◽  
Square Lattice ◽  
Xy Model ◽  
Superfluid Phase ◽  
Zero Temperature ◽  
Ring Exchange

We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson J-K model with nearest neighbour exchange J and four-particle ring-exchange K at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. A similar analysis has been done on a square lattice (Schaffer et al. Phys. Rev. B, 80, 014503 (2009)). We find similar behaviour to that of a square lattice but with different spin wave values of the thermodynamic quantities. We also find that the pure J model (XY model), which has a well-known uniform superfluid phase with an ordered parameter [Formula: see text] at zero temperature is quickly destroyed by the inclusion of negative-K ring-exchange interactions, favouring a state with a (4π/3, 0) ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz–Thouless phase transition (TKT) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for K < 0, the phase boundary monotonically decreases to T = 0 at K/J = −4/3, where a phase transition is expected and TKT decreases rapidly, while for positive K, TKT reaches a maximum at some K ≠ 0. It has been shown on a square lattice using quantum Monte Carlo (QMC) simulations that for small K > 0 away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased (Melko and Sandvik. Ann. Phys. 321, 1651 (2006)). Our result seems to agree with this trend found in QMC simulations for two-dimensional systems.

CRITICAL COARSENING DYNAMICS OF SPIN S =1/2, 3/2 ANTIFERROMAGNETIC ISING MODEL ON TRIANGULAR LATTICE

2006 ◽  
Vol 17 (04) ◽  
pp. 591-600
Author(s):  
KWANGHOON CHUNG ◽  
MOOKYUNG CHEON ◽  
IKSOO CHANG
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Triangular Lattice ◽  
Ground State ◽  
Finite Temperature ◽  
Xy Model ◽  
Two Dimensional ◽  
Type Phase ◽  
Coarsening Dynamics ◽  
Antiferromagnetic Ising Model

The critical coarsening dynamics of the spin S =1/2, 3/2 antiferromagnetic Ising model on a triangular lattice is studied by the dynamic Monte Carlo simulation using a heat bath algorithm. The triangular antiferromagnetic Ising (TAI) model possesses an intrinsic geometrical frustration and a large degeneracy of ground state which may affect the equilibrium and non-equilibrium critical behaviors. The S =1/2 TAI has no phase transition at a finite temperature, but it was suggested that the S =3/2 TAI has the Kosterlitz–Thouless (KT)-type phase transition at a finite temperature. We employ a finite size scaling approach for the correlation function from the short-time dynamics of the S =1/2, 3/2 TAI to calculate the values of the static critical exponent η and the dynamic exponent z. For the S =1/2 TAI, our dynamic scaling analysis provides η =0.498±0.006 and z =2.278±0.020 at T =0, agreeing with the previous results. For the S =3/2 TAI, after identifying a KT-transition temperature TKT =0.51±0.01, we find the temperature-dependent η ranging from 0.301±0.008 at T =0.51 to 0.224±0.016 at T =0 along the KT-line whereas the value of z =2.20±0.06 is constant for T≤TKT. It is shown that the spin S =3/2 TAI model and the two-dimensional XY model, sharing the KT-type phase transition, exhibit similar static critical and coarsening dynamics behavior. For both the S =1/2, 3/2 TAI, the value of z (η) is compatible with (larger than) that of the Ising model at Tc and the XY model for T≤TKT in two-dimension. Our results imply that although the quasi-long-range order disappears with ηXY =0 in the two-dimensional XY model at T =0, the S =3/2 TAI still maintains it with η TAI =0.224 due to the effect of a frustration and a high degeneracy of ground state.

Pinwheel and herringbone structures of planar rotors with anisotropic interactions on a triangular lattice with vacancies

1984 ◽  
Vol 62 (9) ◽  
pp. 915-934 ◽  
Author(s):  
A. B. Harris ◽  
O. G. Mouritsen ◽  
A. J. Berlinsky
Keyword(s):  
Field Theory ◽  
Phase Diagram ◽  
Spin Wave ◽  
Triangular Lattice ◽  
Mean Field Theory ◽  
Mean Field ◽  
Wave Theory ◽  
Finite Domain ◽  
Unexpected Result ◽  
Spin Wave Theory

A variety of theoretical techniques, including Monte Carlo (MC), mean field theory, and spin-wave theory, are used to analyze the phase diagram of a system of planar rotors on a triangular lattice with vacancies. A simple anisotropic interaction, which mimics the electric quadrupole–quadrupole interaction for diatomic molecules confined to rotate in the plane of the surface, induces a herringbone-ordered structure for the pure (x = 1) system, whereas for x ≈ 0.75, if the vacancies are free to move, a 2 × 2 pinwheel structure is favored. For x = 0.75, MC calculations give a continuous transition with Ising exponents in agreement with renormalization group predictions for this universality class, the Heisenberg model with corner-type cubic anisotropy. Mean field theory gives the unexpected result that the pinwheel phase is stable only along the herringbone-disordered state coexistence line in the temperature versus chemical potential phase diagram. Spin-wave theory is used to show that there is, in fact, a finite domain of stability for the pinwheel phase, and a complete phase diagram, which encompasses all available information, is conjectured.

scholarly journals Is there a phase transition in the isotropic Heisenberg anti-ferromagnet on the triangular lattice?

2001 ◽  
Vol 79 (11-12) ◽  
pp. 1459-1461 ◽  
Author(s):  
W Stephan ◽  
B W Southern
Keyword(s):  
Phase Transition ◽  
Triangular Lattice ◽  
Finite Temperature ◽  
Easy Axis ◽  
Temperature Phase ◽  
Temperature Transition ◽  
Isotropic Model ◽  
Temperature Phase Transition ◽  
Lower Temperature ◽  
Xxz Heisenberg Model

The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the two-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-axis limit, two finite-temperature vortex-unbinding transitions have been observed. In the easy-plane limit, there also appear to be two distinct finite-temperature phase transitions that are very close in temperature. The upper transition corresponds to an Ising-like chirality ordering and the lower temperature transition corresponds to a Kosterlitz–Thouless vortex-unbinding transition. These phase-transition lines all meet at the Heisenberg point and provide strong evidence that the isotropic model undergoes a novel finite-temperature phase transition. PACS Nos.: 75.10Hk, 75.40Mg

THE 2-d HEISENBERG MODEL WITH VARIOUS TYPES OF INTERACTIONS: TEMPERATURE DEPENDENCE OF MAGNETIC PARAMETERS AND THE PHASE TRANSITION TEMPERATURE

1993 ◽  
Vol 07 (01n03) ◽  
pp. 504-507
Author(s):  
N. GARCIA ◽  
A. LEVANYUK ◽  
P. SERENA
Keyword(s):  
Phase Transition ◽  
Transition Temperature ◽  
Temperature Dependence ◽  
Spin Wave ◽  
Phase Transition Temperature ◽  
Heisenberg Model ◽  
Wave Theory ◽  
Ferromagnetic Phase ◽  
Temperature Perturbation ◽  
Spin Wave Theory

Using the low-temperature perturbation (spin wave) theory we calculate the temperature dependence of anisotropy constant, spin-wave stiffness, spontaneous magnetization for a two-dimensional ferromagnetic Heisenberg model with various types of anisotropy and interactions. We found that the Polyakov renormalization procedure is inapplicable for ferromagnetic phase at any anisotropy. We did not find the reorientation phase transition due to dipole-dipole interaction predicted by Pescia and Pokrovsky. Taking into account the spin flips we obtained a phase transition temperature in good agreement with results of our Monte Carlo calculations. These results demonstrate also the effectiveness of the spin wave theory.

FINITE TEMPERATURE RESULTS FROM CONSTRAINED FERMIONIZATION IN THE 2-D SPIN 1/2 HEISENBERG ANTIFERROMAGNET I: THE NÉEL PHASE

1994 ◽  
Vol 08 (06) ◽  
pp. 741-756 ◽  
Author(s):  
M. DI STASIO ◽  
A. TAGLIACOZZO ◽  
E. ERCOLESSI ◽  
G. MORANDI
Keyword(s):  
Saddle Point ◽  
Specific Heat ◽  
Spin Wave ◽  
Finite Temperature ◽  
Wave Spectrum ◽  
Site Occupancy ◽  
Zero Point ◽  
Wave Theory ◽  
Heisenberg Antiferromagnet ◽  
Spin Wave Spectrum

The antiferromagnetic saddle point is studied up to one-loop corrections, including, within the same approximation, the constraint of single site occupancy in the fermionization procedure, at all temperatures. The resulting spin wave spectrum and zero point fluctuations are the same as those of the spin wave theory. The effect of the constraint on the temperature dependence of the specific heat is discussed.

scholarly journals Non-hermitian holography

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Daniel Arean ◽  
Karl Landsteiner ◽  
Ignacio Salazar Landea
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Quantum Theory ◽  
Finite Temperature ◽  
Similarity Transformation ◽  
Zero Temperature ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Linear Involution ◽  
Black Hole Solutions

Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one by a Hermitian similarity transformation. We extend the concept of non-Hermitian quantum theory to gauge-gravity duality. Non-Hermiticity is introduced via boundary conditions in asymptotically AdS spacetimes. At zero temperature the PT phase transition is identified as the point at which the solutions cease to be real. Surprisingly at finite temperature real black hole solutions can be found well outside the quasi-Hermitian regime. These backgrounds are however unstable to fluctuations which establishes the persistence of the holographic dual of the PT phase transition at finite temperature.

Modified Spin-Wave Theory of the Bond-DilutedHeisenberg Ferromagnet on a Square Lattice

1991 ◽  
Vol 60 (10) ◽  
pp. 3242-3244
Author(s):  
Fumihisa Suzuki ◽  
Kazuhiro Takayama ◽  
Kazuyuki Watanabe ◽  
Chikara Ishii
Keyword(s):  
Spin Wave ◽  
Wave Theory ◽  
Square Lattice ◽  
Spin Wave Theory
Sign in / Sign up

Export Citation Format

Share Document