Multiplicity of ordered phases in frustrated systems obtained from hard-spin mean-field theory

Abstract

Random quenched dilution of the triangular-lattice antiferromagnetic Ising model locally relieves frustration, leading to ordering phenomena. We have studied this system, under such dilution of one sublattice, using hard-spin mean-field theory. After a threshold dilution, two sublattices develop nonzero magnetizations of equal magnitude and opposite signs, as all three sublattices exhibit spin-glass order. In this phase, multiple sets of ordered solutions occur. A phase diagram is obtained in dilution fraction and temperature.

Successively thresholded domain boundary roughening driven by pinning centers and missing bonds: Hard-spin mean-field theory applied tod=3Ising magnets

“…In our current study, hard-spin mean-field theory [1,2], which has been qualitatively and quantitatively successful in frustrated and unfrustrated, equilibrium and nonequilibrium magnetic ordering problems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], including recently the interface roughening transition [3], is used to study the roughening of an interface by quenched random pinning center sites or missing bonds. The self-consistency equations of hard-spin mean-field theory [2] are…”

The Kinetic Spin-1 Ising System on Triangular Lattice: the Effects of Crystal Field and Frequency of Oscillating External Magnetic Field

“…Therefore, there have been increasing numbers of works dealing with the Ising system on a triangular lattice in the very recently literature (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and references therein). We should also Mehmet Ertaş mehmetertas@erciyes.edu.tr 1 Department of Physics, Erciyes University, 38039 Kayseri, Turkey mention that the spin-1 Ising model on triangular lattice has been also studied using the well-known methods in the equilibrium statistical physics, such as the position-space renormalization group methods [17,[38][39][40][41], finite-size scaling analysis [18], twospin cluster effective field theory (EFT) [19], Monte Carlo simulations [20][21][22][23] and EFT with correlation [24] In spite of these studies, in the best of our knowledge, the dynamic phase transitions and dynamic phase diagrams of kinetic Ising system on triangular lattice have not been investigated.…”

Ground states of the frustrated Blume–Emery–Griffiths model in a field

“…Generally, the lack of order in frustrated spin systems is due to large ground-state degeneracy. However, this can be lifted by various perturbations, such as an external magnetic field [6][7][8][9] or selective dilution [10,11], which can result in long-range ordering even in TLIA with spin 1/2. In the Ising models with spin larger than 1/2, a single-ion anisotropy and higher-order (e.g., biquadratic) exchange interactions may play a crucial role in their critical properties (see, e.g., [12][13][14]).…”