Thermodynamic properties of the triangular-lattice ising antiferromagnet in a uniform magnetic field (original) (raw)
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Physical Review E, 2014
The Pair Approximation method is modified in order to describe the systems with geometrical frustration. The Ising antiferromagnet on triangular lattice with selective dilution (Kaya-Berker model) is considered and a self-consistent thermodynamic description of this model is obtained. For this purpose, the Gibbs free-energy as a function of temperature, concentration of magnetic atoms on the selected sublattice, and external magnetic field is derived. In particular, the phase diagram is constructed and a comparison of different methods is presented. The thermodynamic quantities are discussed in the context of their physical validity and the improvement in the description introduced by modified method is emphasized.
LETTER: Ising antiferromagnets in a nonzero uniform magnetic field
Journal of Statistical Mechanics-theory and Experiment, 2007
We evaluate the density of states g(M,E) as a function of energy E and magnetization M of Ising models on square and triangular lattices, using the exact enumeration method for small systems and the Wang Landau method for larger systems. From the density of states the average magnetization per spin, m(T,h), of the antiferromagnets has been obtained for any values of temperature T and uniform magnetic field h. Also, based on g(M,E), the behaviour of m(T,h) is understood microcanonically. The microcanonical approach reveals the differences between the unfrustrated model (on the square lattice) and the frustrated one (on the triangular lattice).
Arxiv preprint arXiv: …, 2010
The partition functions for two-dimensional nearest neighbour Ising model in a non-zero magnetic field have been derived for finite square lattices with the help of graph theoretical procedures, show-bit algorithm, enumeration of configurations and transfer matrix methods. A new recurrence relation valid for all lattice sizes is proposed. A novel method of computing the critical temperature has been demonstrated. The magnetization and susceptibility for infinite lattices in the presence of magnetic field is estimated. The critical exponent δ pertaining to the magnetization has also been computed. 120 576 2112 3264 J J J J J kT kT kT kT kT J J J J kT kT kT kT c c c c J J J J J kT kT kT kT kT J J J J c kT kT kT kT
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.
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.
Physical Review B, 2006
We calculate the density of states for the face-centered-cubic ͑fcc͒ Ising model with nearest-neighbor interactions using a Wang-Landau algorithm. This allows us to calculate thermodynamic quantities at all temperatures for both the ferromagnetic ͑FM͒ and antiferromagnetic ͑AF͒ models from the same data set, while avoiding the hysteresis usually occurring in models undergoing a first-order phase transition. For the FM model, our results are in agreement with high-temperature ͑HT͒ series expansion results, and are of the same precision. For the AF model which has a first-order transition, and where precise estimates of the critical behavior are lacking, we obtain T N = 1.7217͑8͒. We also obtain estimates of the free energy, internal energy, and entropy of both the ordered and disordered states at T N with a precision comparable to that obtained in the HT series for the FM model. Details of the finite-size scaling for the AF model are discussed, and a different convergence criterion for the Wang-Landau method is introduced.
Nuclear Physics B, 2008
The grand partition functions Z(T , B) of the Ising model on L × L triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B, are evaluated exactly for L < 12 (using microcanonical transfer matrix) and approximately for L 12 (using Wang-Landau Monte Carlo algorithm). From Z(T , B), the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B = 0 are obtained and discussed for the first time. The critical points a N (x) and the thermal scaling exponents y t (x) of the triangular-lattice Ising antiferromagnet, for various values of x = e −2βB , are estimated using the partition function zeros.
Some magnetic properties of the diluted square ising lattice with fluctuating exchange integrals
Journal of Magnetism and Magnetic Materials, 1990
The site-and bond-disordered ferromagnet is examined with the use of the 1st and 3rd Matsudaira approxivaations. As a result, the phase diagrams, the magnetization curves and the correlation functions between nearest neighbour spins for various c and A parameters, characterizing the dilution and the fluctuations of the exchange integral, are discussed in detail.
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...
Ising Model Phase Transition Calculation for Ferro-Paramagnetic Lattice
International Letters of Chemistry, Physics and Astronomy, 2013
The position of the phase transition in the two dimensional Ising model were determined byusing Monte Carlo simulation in a quadratic for area of variable length with external magnetic fieldswitched off (B = 0). The magnetization (M) per site (µ), magnetic susceptibility (x) of aferromagnetic and paramagnetic materials were calculated as a function of temperature T for(20×20,40×40,60×60), (80×80,120×120,200×200) spin lattice interactions. Nearest neighborinteraction is assumed (i.e. each spin has 4 neighbors); uses periodic boundary conditions. The Curietemperature (Tc = 2.27 J/kB ) is determined by measuring the magnetic susceptibility at which theferromagnetic and paramagnetic undergoes a phase change from order to disorder. There is thus aphase transition defined by the Curie temperature. The Monte Carlo method were used to check theseresults and to confirm the phase transition. The data are analyzed using the Curie-Weiss law whichcontains the Curie temperature as a parameter.