Phase transitions, order by disorder, and finite entropy in the Ising antiferromagnetic bilayer honeycomb lattice

Abstract

We present an analytical and numerical study of the Ising model on a bilayer honeycomb lattice including interlayer frustration and coupling with an external magnetic field. First, we discuss the exact T=0 phase diagram, where we find finite entropy phases for different magnetizations. Then, we study the magnetic properties of the system at finite temperature using complementary analytical techniques (Bethe lattice) and two types of Monte Carlo algorithms (Metropolis and Wang-Landau). We characterize the phase transitions and discuss the phase diagrams. The system presents a rich phenomenology: There are first- and second-order transitions, low-temperature phases with extensive degeneracy, and order-by-disorder state selection.

Magnetic behavior of a ferroferrimagnetic ternary alloy ABρC1−ρ with a selective site disorder: Case study of a mixed-spin Ising model on a honeycomb lattice

“…where ε = σ i σ j t denotes the nearest-neighbor pair correlation function of the effective spin-1/2 Ising model on a triangular lattice given by the effective Hamiltonian (16). After some algebraic manipulations, one may express the concentration ρ of the spin-1 magnetic ions in the following compact form:…”

“…In this section we will establish finite-temperature phase diagrams of the mixed-spin Ising ternary alloy on a selectively diluted honeycomb lattice. To this end, it is sufficient to realize that the mapping relation (15) between the grand-canonical partition function of the mixed-spin Ising ternary alloy on a selectively diluted honeycomb lattice shows a singularity only if the same singularity appears in the canonical partition function of the effective spin-1/2 Ising model on a triangular lattice given by the Hamiltonian (16). It should be pointed out that the critical parameters for the spin-1/2 Ising model on a triangular lattice are known exactly (for review see for instance Refs.…”

“…The binary mixed-spin Ising systems are the simplest models allowing a theoretical description of the main characteristics of ferrimagnetism. To date, there are numerous theoretical studies of the binary mixed-spin Ising models defined on a honeycomb lattice [6][7][8][9][10][11][12][13][14][15][16][17], bathroom-tile lattice [18,19], diced lattice [20], square lattice [21][22][23][24][25], Bethe lattice [26,27], etc. As far as spin sizes are concerned, the binary mixed-spin Ising models with a great variety of combinations of the spin magnitudes have been investigated as, for instance, (1/2, 1) [6,7,13,14,20], (1/2, 3/2) [8,21], (1, 3/2) [9,10], (1/2, S > 1/2) [11,18,22], (2, 5/2) [12,15], (3/2, 2) [26], (7/2, 1) [23,27], (7/2, 2) [24] and (7/2, 3) [25].…”

“…As far as spin sizes are concerned, the binary mixed-spin Ising models with a great variety of combinations of the spin magnitudes have been investigated as, for instance, (1/2, 1) [6,7,13,14,20], (1/2, 3/2) [8,21], (1, 3/2) [9,10], (1/2, S > 1/2) [11,18,22], (2, 5/2) [12,15], (3/2, 2) [26], (7/2, 1) [23,27], (7/2, 2) [24] and (7/2, 3) [25]. Magnetic properties of the binary mixed-spin Ising models on a honeycomb lattice were exploited by various theoretical methods such as exact mapping technique [6,8], Monte Carlo simulations [12,13,16,21], cluster variational method [29], effective- [9] and mean-field [28] theories.…”

Multiple pseudo-plateaux states and antiferromagnetic pair selection in the XY model in the highly frustrated honeycomb lattice

“…In addition, there has been a large body of work devouted to the studies of models with long range competing exchange and Kitaev interactions, due to the experimental evidence in materials like α − RuCl 3 and Na 2 IrO 3 (for recent reviews see for example reference [8]). Exchange interactions beyond second nearest neighbors have been shown to give rise to different phenomena depending on the types of spins considered: classical Ising spins [9], quantum spins [10], XY spins [11], etc. Additional interactions may also give rise to interesting phenomena depending on the geometry of the lattice, such as the square lattice [12][13][14], or highly frustrated ones, as the kagome lattice [15][16][17].…”