We study instantaneous quenches from infinite temperature to well below $T_c$ in the two-dimensional square lattice Ising antiferromagnet in the presence of a longitudinal external magnetic field. Under single-spin-flip Metropolis algorithm Monte Carlo dynamics, this protocol produces a pair of magnetization plateaus that prevent the system from reaching the equilibrium ground state except for some special values of the field. We explain the plateaus in terms of local spin configurations that are stable under the dynamics.
Recent studies have revealed that the randomness-induced quantum spin liquid (QSL)-like state is stabilized in certain frustrated quantum magnets in two and three dimensions. In order to clarify the nature of this gapless QSL-like state, we investigate both zero- and finite-temperature properties of the random-bond one-dimensional (1D) $s=12$ Heisenberg model with the competing nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and $J_2$, by means of the exact diagonalization, density-matrix renormalization-group and Hams--de Raedt methods. We find that, on increa…
We study Ising antiferromagnets that have nearest-neighbour interactions on multilayer triangular lattices with frustrated ($abc$ and $abab$) stacking, and make comparisons with the unfrustrated ($aaa$) stacking. If interlayer couplings are much weaker than in-plane ones, the paramagnetic phase of models with frustrated stackings has a classical spin-liquid regime at low temperature, in which correlations are strong both within and between planes, but there is no long-range order. We investigate this regime using Monte Carlo simulations and by mapping the spin models to coupled height models, …
We investigate the consequences for geometrically frustrated antiferromagnets of weak disorder in the strength of exchange interactions. Taking as a model the classical Heisenberg antiferromagnet with nearest neighbour exchange on the pyrochlore lattice, we examine low-temperature behaviour. We show that random exchange generates long-range effective interactions within the extensively degenerate ground states of the clean system. Using Monte Carlo simulations, we find a spin glass transition at a temperature set by the disorder strength. Disorder of this type, which is generated by random str…
We study critical and magnetic properties of a bilayer Ising system consisting of two triangular planes A and B, with the antiferromagnetic (AF) coupling $J_{\rm A}$ and the ferromagnetic (FM) one $J_{\rm B}$ for the respective layers, which are coupled by the interlayer interaction $J_{\rm AB}$ by using Monte Carlo simulations. When $J_{\rm A}$ and $J_{\rm B}$ are of the same order, the unfrustrated FM plane orders first at a high temperature $T_{c1} \sim J_{\rm B}$. The spontaneous FM order then exerts influence on the other frustrated AF plane as an effective magnetic field, which subsequen…
We calculate the spin stiffness of the S=1/2 frustrated Heisenberg antiferromagnet directly from a general formula which is evaluated in the Schwinger boson mean-field approximation. Both Néel and collinear ordering are considered. For collinear ordering, we take the anisotropy of this phase into account, unlike previous approaches. For Néel ordering, a detailed study is made of the finite-size scaling behavior of the two terms that make up the spin stiffness. The exponents of the scaling with the system size of the two terms comprising the spin stiffness turn out to be identical to those of t…
We study the possibility of long-range ordering (LRO) in a 3D system of vertically stacked layers of Ising antiferromagnet on a kagome lattice (SIAKL). Monte Carlo simulations are carried out for a varying interlayer coupling strength and a finite-size scaling analysis is performed for selected cases. Unlike in the related Ising system on a triangular lattice, in which even a finite number of the layers can stabilize LRO, or the Heisenberg system on the same kagome lattice, in which LRO emerged in 3D for a sufficient strength of the interlayer coupling, no LRO could be observed in the present …
The antiferromagnetic Ising model is investigated on the 20 2-uniform lattices using the Monte-Carlo method based on the Wang-Landau algorithm and the Metropolis algorithm to study the geometric frustration effect systematically. Based on the specific heat, the residual entropy, and the Edwards-Anderson freezing order parameter, the ground states of them were determined. In addition to the long-range-ordered phase and the spin ice phase found in the Archimedean lattices, two more phases were found. The partial long-range order is long-range order with exceptional disordered sites, which gives …
We study the correlation function of middle spins, i. e. of spins on intermediate sites between two adjacent parallel lattice axes, of the spatially anisotropic Ising antiferromagnet on the kagome lattice. It is given rigorously by a Toeplitz determinant. The large-distance behaviour of this correlation function is obtained by analytic methods. For shorter distances we evaluate the Toeplitz determinant numerically. The correlation function is found to vanish exactly on a line J_d(T) in the T-J (temperature vs. coupling constant) phase diagram. This disorder line divides the phase diagram into …
We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbour antiferromagnetic interactions on a class of geometrically frustrated lattices which includes the kagome and pyrochlore lattices. We explore the behaviour of these magnets that results from their large ground-state degeneracies, emphasising universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest…
Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte-Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly-frustrated and have two-dimensional and one-dimensional long-range-ordered ground s…
Experimental quest for the hypothetical "quantum spin liquid" state has recently met a few promising candidate materials including organic salts κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, S=1/2 triangular-lattice Heisenberg antiferromagnets consisting of molecular dimers. These compounds exhibit no magnetic ordering nor the spin freezing down to very low temperature, while various physical quantities exhibit gapless behaviors. Recent dielectric measurements revealed the glassy dielectric response suggesting the random freezing of the electric polarization degrees of freedom. Inspired by this obs…
We study the effect of antiferromagnetic interactions on the single spin-flip Glauber dynamics of two different one-dimensional (1D) Ising models with spin $\pm 1$. The first model is an Ising chain with antiferromagnetic exchange interaction limited to nearest neighbors and subject to an oscillating magnetic field. The system of master equations describing the time evolution of sublattice magnetizations can easily be solved within a linear field approximation and a long time limit. Resonant behavior of the magnetization as a function of temperature (stochastic resonance) is found, at low freq…
For Ising spin models which bear the spin-ice type macroscopic (quasi-)degeneracy, conventional classical Monte Carlo (MC) simulation using single spin flips suffers from dynamical freezing at low temperatures ($T$). A similar difficulty is seen also in a family of Heisenberg spin models with easy-axis anisotropy or biquadratic interactions. In the Ising case, the difficulty is avoided by introducing a non-local update based on the loop algorithm. We present an extension of the loop algorithm to the Heisenberg case. As an example of its application, we review our recent study on spin-glass (SG…
We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferro- and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents $γ/ν$, $α/ν$ and $ν$ to be obtained, whenever a second-order transition is present. Low-temperature ordering persists for suitably small concentrations of frustrated bonds, with a transition governed by pure--Ising exponents. Cont…
Magnetization process and adiabatic demagnetization of the antiferromagnetic Ising spin clusters with the shape of regular polyhedra (Platonic solids) are exactly examined within the framework of a simple graph-theoretical approach. While the Ising cube as the only unfrustrated (bipartite) spin cluster shows just one trivial plateau at zero magnetization, the other regular Ising polyhedra (tetrahedron, octahedron, icosahedron and dodecahedron) additionally display either one or two intermediate plateaux at fractional values of the saturation magnetization. The nature of highly degenerate groun…
The interplay between geometric frustration (GF) and bond disorder is studied in the Ising kagome lattice within a cluster approach. The model considers antiferromagnetic (AF) short-range couplings and long-range intercluster disordered interactions. The replica formalism is used to obtain an effective single cluster model from where the thermodynamics is analyzed by exact diagonalization. We found that the presence of GF can introduce cluster freezing at very low levels of disorder. The system exhibits an entropy plateau followed by a large entropy drop close to the freezing temperature. In t…
The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelas…
We study the nature of a low-temperature phase in the frustrated honeycomb-lattice Ising model with first- and second-neighbor antiferromagnetic (AF) interactions, $J_1$ and $J_2$, respectively, for $R = J_2/J_1 > 1/4$. It is known that for $R < 1/4$ there is a phase transition at low temperatures to the AF phase. Nevertheless, little is known about the critical behavior of the model for $R > 1/4$, except for recent effective field results which detected no phase transition down to zero temperature. Our Monte Carlo results suggest that for $R > 1/4$ there is at least one peculiar phase transit…
