Residual entropy of spin-s triangular Ising antiferromagnet

We employ a thermodynamic integration method (TIM) to establish the values of the residual entropy for the geometrically frustrated spin-s triangular Ising antiferromagnet, with the spin values s = 1/2, 1, 3/2, 2 and 5/2. The case of s = 1/2, for which the exact value is known, is used to assess the TIM performance. We also obtain an analytical formula for the lower bound in a general spin-s model and conjecture that it should reasonably approximate the true residual entropy for sufficiently large s. Implications of the present results in relation to reliability of the TIM as an indirect method for calculating global thermodynamic quantities, such as the free energy and the entropy, in similar systems involving frustration and/or higher spin values by standard Monte Carlo sampling are briefly discussed.     

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     

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.     

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.     

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.     

Weak Disorder Localization and Lifshitz Tails

 This paper is devoted to the study of localization of discrete random Schr?dinger Hamiltonians in the weak disorder regime. Consider an i.i.d. Anderson model and assume that its left spectral edge is 0. Let γ be the coupling constant measuring the strength of the disorder. For γ small, we prove a Lifshitz tail type estimate and use it to derive localization in a band starting at 0 going up to a distance of the average of the potential. In this energy region, we show that the localization length at energy E is bounded from above by a constant times the square root of the distance between E and the average of the potential.

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Résumé . Dans cet article, nous étudions la localisation à faible désordre pour des opérateurs de Schr?dinger aléatoires discrets. Considérons un modèle d'Anderson i.i.d. dont le bord spectral gauche vaut 0. Soit γ la constante de couplage mesurant le désordre. Pour γ petit, nous démontrons une estimée de type estimée de Lifshitz pour la densité d'états, et nous utilisons cette estimée pour prouver que le spectre de cet opérateur est localisé dans un intervalle allant de l'énergie 0 jusqu'à une distance de l'ordre de de la moyenne du potentiel. Dans cette région d'énergie, la longueur de localisation à une énergie E est majorée par une constante fois la racine de la distance séparant E de la moyenne du potentiel.

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Received: 7 December 2001 / Accepted: 26 July 2002 Published online: 29 October 2002

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ID="*" It is a pleasure to thank M. Aizenman for his explanations on the paper [4]. The author also gratefully acknowledges support of the FNS 2000 ``Programme Jeunes Chercheurs'     

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)     

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.     

Magnetic properties of Heisenberg triangular antiferromagnet V15 cluster studied by NMR

The magnetic properties of an s?=?1/2 Heisenberg triangular antiferromagnet V15 have been studied by proton nuclear magnetic resonance (NMR) at very low temperature down to 100 mK using a He³-He⁴ dilution refrigerator. In total spin S _T?=?3/2 ground state above 2.7 Tesla, proton spin-lattice relaxation rate (1/T₁) shows thermally activated behavior as a function of temperature. On the other hand, a temperature independent behavior of 1/T₁ at very low temperatures is observed in frustrated S _T?=?1/2 ground state below 2.7 Tesla. Possible origins for the peculiar behavior of 1/T₁ will be discussed in terms of magnetic fluctuations due to spin frustration.     

Thermodynamics properties of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H$H$ and transverse magnetic field Ω$\Omega$. Using the effective-field theory (EFT) with correlation in cluster with N=1$N=1$ spin we calculate the thermodynamic properties as a function of temperature with values H$H$ and Ω$\Omega$ fixed. The model consists of ferromagnetic interaction _Jx$J_x$ in the x$x$ direction and antiferromagnetic interaction _Jy$J_y$ in the y$y$ direction, and it is found that for H/_Jy∈[0,2]$H/J_y\in [0,2]$ the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$ (isotropic square lattice).     

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.     

Lifshitz Asymptotics via Linear Coupling of Disorder

We present a simple method for proving Lifshitz asymptotics for random Schrödinger operators and apply it to the Anderson and Poisson model.