Effective field theory of the zero-temperature triangular-lattice antiferromagnet: A Monte Carlo study (original) (raw)
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Monte Carlo study of a compressible Ising antiferromagnet on a triangular lattice
Physical review. B, Condensed matter, 1996
We have studied the compressible antiferromagnetic Ising Model on a triangular lattice using Monte Carlo simulations. It is found that the coupling to the strain removes the frustration of the rigid model and the simulations show a transition from the disordered to an ordered, striped phase at low temperatures. This transition involves two broken symmetries: the Ising symmetry and a three-state Potts symmetry characteristic of the triangular lattice. In the absence of bond fluctuations, this transition is always strongly first order. Using finite-size scaling analysis, we find evidence that, in the presence of fluctuations, the transition becomes weakly first order and possibly second order when the coupling to the lattice is increased. We discuss the relevance of this model to certain phase transitions in alloys.
Multiple-histogram Monte Carlo study of the Ising antiferromagnet on a stacked triangular lattice
Physical Review B, 1993
The nearest neighbor Ising antiferromagnet on a stacked triangular lattice is a frustrated cooperative system in which it is known that at least two long-range ordered states exist at low temperature. This model has also been of considerable interest as it is known to be a reasonable description of two antiferromagnetic insulators, CsCoBrs and CsCoC13. It has also been the subject of previous theoretical and simulation studies which have yielded con8icting results for the critical phenomena displayed near the transition from the paramagnetic to the high-temperature ordered phase. We have carried out a detailed Monte Carlo study of this system using the recently developed multiplehistogram technique and finite-size scaling analysis, with the purpose of extracting estimates for the critical exponents relevant to this continuous transition. Our results give P = 0.311(4), p = 1.43(3), o. =-0.05(3), and v = 0.685(3) which are not in agreement with previous Monte Carlo work. In addition, although they are close to the expectations from previous symmetry arguments, there are systematic differences between our results and these theoretical predictions. A possible interpretation of these Monte Carlo exponent estimates is that they do not correspond to those calculated for any known universality class, and add to the growing number of simple models of interacting spins, in which geometrical frustration is relevant, which appear to exhibit novel critical behavior. Finally, we have examined the evolution of real-space spin configurations and have seen that a buildup of correlations between anti-phase-domain walls, or solitons, along the stacking direction precedes the transition, an observation which is consistent with recent neutron-scattering measurements on CsCoBr3.
Physical review. B, Condensed matter, 1993
Critical properties of the Ising model on a stacked triangular lattice, with antiferromagnetic first and second-neighbor in-plane interactions, are studied by extensive histogram Monte Carlo simulations. The results, in conjunction with the recently determined phase diagram, strongly suggest that the transition from the period-3 ordered state to the paramagnetic phase remains in the xy universality class. This conclusion is in contrast with a previous suggestion of mean-field tricritical behavior.
Ground states of the antiferromagnetic Ising model on finite triangular lattices of simple shape
Physics Letters A, 2003
The ground state energy of the antiferromagnetic Ising model on finite triangular lattices of some simple shapes is derived using simple arguments. It is shown that the ground state entropy density vanishes for a parallelogram with a free boundary. Numerical calculation of the ground state entropy density for some other simple shapes with free boundaries illustrates the approach to the thermodynamic limit. The results illustrate, by explicit examples, the known intricate relationship between boundary conditions, degeneracy and the ground state entropy in the thermodynamic limit. They are also relevant to some applications of the Ising model in biophysics.
Thermodynamic properties of the triangular-lattice ising antiferromagnet in a uniform magnetic field
Using both the exact enumeration method (microcanonical transfer matrix) for small systems (up to 9 ¢ 9 lattices) and the Wang-Landau Monte Carlo algorithm for large systems (up to 30 ¢ 30 lattices), we obtain the exact and approximate densities of states g(M; E), as a function of magnetization M and exchange energy E, for the triangular-lattice Ising model in the presence of an external uniform magnetic eld. The method for evaluating the exact density of states g(M; E) of the triangular-lattice Ising model is introduced for the rst time. Based on the density of states g(M; E), we investigate the properties of the various thermodynamic quantities as a function of temperature T and magnetic eld h and nd the phase diagram of the Ising antiferromagnet in the magnetic eld. In addition, the zero-temperature thermodynamic properties are studied by reference to the density of states at the corner or along the edge line on the magnetization-energy (ME) diagram.
The Ising antiferromagnet on an anisotropic simple cubic lattice in the presence of a magnetic field
arXiv: Statistical Mechanics, 2012
We have studied the anisotropic three-dimensional nearest-neighbor Ising model with competitive interactions in an uniform longitudinal magnetic field HHH. The model consists of ferromagnetic interaction Jx(Jz)J_{x}(J_{z})Jx(Jz) in the x(z)x(z)x(z) direction and antiferromagnetic interaction JyJ_{y}Jy in the yyy direction. We have compared our calculations within a effective-field theory in clusters with four spins (EFT-4) in the simple cubic (sc) lattice with traditional Monte Carlo (MC) simulations. The phase diagrams in the h−kBT/Jxh-k_{B}T/J_{x}h−kBT/Jx plane ($h=H/J_{x}$) were obtained for the particular case lambda1=Jy/Jx(lambda2=Jz/Jx)=1\lambda_{1}=J_{y}/J_{x} (\lambda_{2}=J_{z}/J_{x})=1lambda1=Jy/Jx(lambda2=Jz/Jx)=1 (anisotropic sc). Our results indicate second-order frontiers for all values of HHH for the particular case lambda2=0\lambda_{2}=0lambda2=0 (square lattice), while in case lambda1=lambda2=1\lambda_{1}=\lambda_{2}=1lambda1=lambda2=1, we observe first- and second-order phase transitions in the low and high temperature limits, respectively, with presence of a tricritical point. Using EFT-4, a reentran...
Latent heat of the fcc Ising antiferromagnet
Journal of Applied Physics, 2007
To obtain critical parameters of the fcc Ising antiferromagnet from Monte Carlo data, a numerical estimate of the latent heat ⌬ is required. The precision of current estimates is about 3%, and ultimately limits the precision achieved for the disordered state at the Néel temperature T N. Here we make several different estimates of the latent heat, using finite size scaling of Monte Carlo data, and show that a superior method yields a 25-fold improvement ͓⌬ = 0.4559͑6͔͒ in comparison with our older result ͓⌬ = 0.455͑15͔͒.
Theory of the kagome lattice Ising antiferromagnet in weak transverse fields
2005
We study the quantum Ising antiferromagnet on the Kagome lattice, with weak transverse field dynamics and other local perturbations. We analytically demonstrate the possibility of a disordered zero-temperature phase that is smoothly connected to the phase at strong transverse fields. This is done by means of an appropriate mapping to a compact U(1) gauge theory on the honeycomb lattice that is coupled to a charge-1 matter field. Our results are consistent with existing Monte-Carlo calculations. The differences with other commonly studied lattices (in which such disordered phases do not obtain at weak transverse fields) is explained. Ordered phases are also shown to be possible in principle in the weak transverse field limit, and are briefly studied.
Triangular Ising antiferromagnet in a staggered field
Physical Review B, 2000
We study the equilibrium properties of the nearestneighbor Ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states. Using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice, we classify the ground states into sectors specified by the number of "strings". We show that the effect of the staggered field is to generate long-range interactions between strings. In the limiting case of the antiferromagnetic coupling constant J becoming infinitely large, we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature. For finite J, we study the equilibrium properties of the system using Monte Carlo simulations with three different dynamics. We find that in all the three cases, equilibration times for low field values increase rapidly with system size at low temperatures. Due to this difficulty in equilibrating sufficiently large systems at low temperatures, our finite-size scaling analysis of the numerical results does not permit a definite conclusion about the existence of a phase transition for finite values of J. A surprising feature in the system is the fact that unlike usual glassy systems, a zero-temperature quench almost always leads to the ground state, while a slow cooling does not.
Low temperature properties of the triangular-lattice antiferromagnet: A bosonic spinon theory
2012
We study the low temperature properties of the triangular-lattice Heisenberg antiferromagnet with a mean field Schwinger spin-1 2 boson scheme that reproduces quantitatively the zero temperature energy spectrum derived previously using series expansions. By analyzing the spin-spin and the boson density-density dynamical structure factors, we identify the unphysical spin excitations that come from the relaxation of the local constraint on bosons. This allows us to reconstruct a free energy based on the physical excitations only, whose predictions for entropy and uniform susceptibility seem to be reliable within the temperature range 0 T 0.3J , which is difficult to access by other methods. The high values of entropy, also found in high temperature expansion studies, can be attributed to the roton-like narrowed dispersion at finite temperatures.