Residual entropy of the one-dimensional Ising antiferromagnet with general spin

We have calculated the ground-state degeneracy and the concominant residual entropy of the one-dimensional Ising antiferromagnet in a critical magnetic field. We demonstrate that the results obtained can be related to the ground-state properties of the q-state Potts antiferromagnet in the corresponding external field.     

Solving the triangular Ising antiferromagnet by simple mean field

Few years ago, application of the mean field Bethe scheme on a given system was shown to produce a systematic change of the system intrinsic symmetry. For instance, once applied on a ferromagnet, individual spins are no more equivalent. Accordingly a new loopwise mean field theory was designed to both go beyond the one site Weiss approach and yet preserve the initial Hamitonian symmetry. This loopwise scheme is applied here to solve the triangular antiferromagnetic Ising model. It is found to yield Wannier's exact result of no ordering at non-zero temperature. No adjustable parameter is used. Simultaneously a non-zero critical temperature is obtained for the triangular Ising ferromagnet. This simple mean field scheme opens a new way to tackle random systems. Received 14 November 2001 / Received in final form 22 March 2002 Published online 19 July 2002     

Low-temperature metastable states in a stacked triangular Ising antiferromagnet

We study low-temperature magnetization processes in a stacked triangular Ising antiferromagnet by Monte Carlo simulations. In increasing and decreasing magnetic fields we observe multiple steps and hysteresis corresponding to formation of different metastable states. Besides the equidistant threefold splitting of the 1/3 ferrimagnetic plateau, we additionally confirm a fourth plateau in the field-increasing branch and a sizable remanence when the field is decreased to zero. The newly observed plateau only appears at sufficiently low temperature and sufficiently large exchange interaction in the stacking direction. These observations reasonably reproduce low-temperatures measurements on the spin-chain compound Ca₃Co₂O₆.     

Phase diagram of a diluted triangular lattice Ising antiferromagnet in a field

Magnetization processes and phase transitions in a geometrically frustrated triangular lattice Ising antiferromagnet in the presence of an external magnetic field and a random site dilution are studied by the use of an effective-field theory with correlations. We find that the interplay between the applied field and the frustration-relieving dilution results in peculiar phase diagrams in the temperature-field-dilution parameter space.     

Critical and tricritical behavior of a selectively diluted triangular Ising antiferromagnet in a field

We study a geometrically frustrated triangular Ising antiferromagnet in an external magnetic field which is selectively diluted with nonmagnetic impurities employing an effective-field theory with correlations and Monte Carlo simulations. We focus on the frustration-relieving effects of such a selective dilution on the phase diagram and find that it can lead to rather intricate phase diagrams in the dilution-field parameters space. In particular, in a highly (weakly) diluted system the frustration is greatly (little) relieved and such a system is found to display only the second(first)-order phase transitions at any field. On the other hand, for a wide interval of intermediate dilution values the transition remains second-order at low fields but it changes to first-order at higher fields and the system displays a tricritical behavior. The existence of the first-order transition in the region of intermediate dilution and high fields is verified by Monte Carlo simulations.     

Thermodynamic and critical properties of an antiferromagnetically stacked triangular Ising antiferromagnet in a field

We study a stacked triangular lattice Ising model with both intra- and inter-plane antiferromagnetic interactions in a field, by Monte Carlo simulation. We find only one phase transition from a paramagnetic to a partially disordered phase, which is of second order and 3D XY universality class. At low temperatures we identify two highly degenerate phases: at smaller (larger) fields the system shows long-range ordering in the stacking direction (within planes) but not in the planes (stacking direction). Nevertheless, crossovers to these phases do not have a character of conventional phase transitions but rather linear-chain-like excitations.     

Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions

Using a Wang-Landau entropic sampling scheme, we investigate the effects of quenched bond randomness on a particular case of a triangular Ising model with nearest- (J_nn) and next-nearest-neighbor (J_nnn) antiferromagnetic interactions. We consider the case R=J_nnn/J_nn=1, for which the pure model is known to have a columnar ground state where rows of nearest-neighbor spins up and down alternate and undergo a weak first-order phase transition from the ordered to the paramagnetic state. With the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first-order phase transition to a second-order phase transition and using the Lee-Kosterlitz method, we quantitatively verify this conversion. The emerging, under random bonds, continuous transition shows a strongly saturating specific heat behavior, corresponding to a negative exponent α, and belongs to a new distinctive universality class with ν=1.135(11), γ/ν=1.744(9), and β/ν=0.124(8). Thus, our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional (2d) systems without and with quenched disorder.     

Metamagnetic transitions in an Ising antiferromagnet

An Ising antiferromagnet of arbitrary spin is examined in the molecular field approximation. It is found that the field induced transition can be of four different types: second order, first order, a first order followed by a second order and two successive first order, depending on the temperature and the ratio of the nn to nnn exchange interactions. Landau's theory of second order phase transition in conjunction with a detailed examination of the behavior of the free energy is employed to map the regions of the different types of transition.     

Effects of selective dilution on phase diagram and ground-state magnetizations of an Ising antiferromagnet on triangular and honeycomb lattices

We employ an effective-field theory with correlations in order to study the phase diagram and ground-state magnetizations of a selectively diluted Ising antiferromagnet on triangular and honeycomb lattices. Dilution of different sublattices with generally unequal probabilities results in a rather intricate phase diagram in the sublattice dilution parameters space. In the case of the frustrated triangular lattice antiferromagnet the selective dilution affects the degree of frustration which can lead to some peculiar phenomena, such as reentrant behavior of long-range order or unsaturated sublattice magnetizations at zero temperature. The selectively diluted Ising antiferromagnet on the honeycomb lattice is obtained as a special case when one sublattice of the triangular lattice is completely removed by dilution.     

Monte Carlo simulation of a random-field Ising antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.     

Yang-Lee zeros of triangular Ising antiferromagnets

In our previous research, by combining both the exact enumeration method (microcanonical transfer matrix) for a small system (L=9) with the Wang-Landau Monte Carlo algorithm for large systems (to L=30) we obtained the exact and approximate densities of states g(M,E), as a function of the magnetization M and exchange energy E, for a triangular-lattice Ising model. In this paper, based on the density of states g(M,E), the precise distribution of the Yang-Lee zeros of triangular-lattice Ising antiferromagnets is obtained in a uniform magnetic field as a function of temperature for a 9×9 lattice system. Also, the feasibility of the Yang-Lee zero approach combined with the Wang-Landau algorithm is demonstrated; as a result, we obtained the magnetic exponents for triangular Ising antiferromagnets at various temperatures.     

On the magnetic structure of a hexagonal Ising antiferromagnet

Domain wall free energies are calculated in a hexagonal Ising antiferromagnet and shown to be very small compared with those in an ordinary two-sublattice antiferromagnet. It is suggested that the magnetic structure of its higher temperature ordered phase is one in which many domains are tangled with each other. Some comments are given on experimental results in CsCoCl₃ and CsCoBr₃.     

Metamagnetism and magnetostriction of the Ising antiferromagnet DyCrO3

The magnetostriction of the Ising antiferromagnet DyCrO₃ during metamagnetic transitions induced by a magnetic field applied along the a and b axes of the crystal is investigated experimentally and theoretically. The magnetostriction measurements performed in the temperature range 1.5–4.2 K in magnetic fields up to 3 T clearly reveal the two-step character of the transition from the original antiferromagnetic structure to the ferromagnetic structure with the intermediate formation of a low-symmetry structure (when H is parallel to the a axis). The unusual behavior of the magnetostriction discovered during the magnetizing process provides information on the nature of magnetostriction in rare-earth Ising metamagnets. Fiz. Tverd. Tela (St. Petersburg) 39, 668–670 (April 1997)     

Unconventional dynamics in triangular Heisenberg antiferromagnet NaCrO2

We report magnetization, specific heat, muon spin rotation, and Na NMR measurements on the S=3/2 rhombohedrally stacked Heisenberg antiferromagnet NaCrO2. This compound appears to be a good candidate for the study of isotropic triangular Heisenberg antiferromagnets with very weak interlayer coupling. While specific heat and magnetization measurements indicate the onset of a transition in the range Tc approximately 40-50 K, both muon spin rotation and NMR reveal a fluctuating crossover regime extending well below Tc, with a peak of relaxation rate T1(-1) around T approximately 25 K. This novel finding is discussed within the context of excitations in the triangular Heisenberg antiferromagnets.