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Register a new userMixed Ising ferrimagnets with next-nearest neighbour couplings on square lattices
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We study Ising ferrimagnets on square lattices with antiferromagnetic exchange couplings between spins of values S=1/2 and S=1 on neighbouring sites, couplings between S=1 spins at next--nearest neighbour sites of the lattice, and a single--site anisotropy term for the S=1 spins. Using mainly ground state considerations and extensive Monte Carlo simulations, we investigate various aspects of the phase diagram, including compensation points, critical properties, and temperature dependent anomalies. In contrast to previous belief, the next--nearest neighbour couplings, when being of antiferromagnetic type, may lead to compensation points.
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This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions interactions arise naturally in several applications such as the colour diversity problem and graphical games. We demonstrate ensembles of random graphs, including regular connectivity graphs, that have a periodic variation of free energy, with either the ratio of nearest to next nearest couplings, or the mean number of nearest neighbours. When the coupling ratio is integer paramagnetic phases can be found at zero temperature. This is shown to be related to the locked or unlocked nature of the interactions. For anti-ferromagnetic couplings, spin glass phases are demonstrated at low temperature. The interaction structure is formulated as a factor graph, the solution on a tree is developed. The replica symmetric and energetic one-step replica symmetry breaking solution is developed using the cavity method. We calculate within these frameworks the phase diagram and demonstrate the existence of dynamical transitions at zero temperature for cases of anti-ferromagnetic coupling on regular and inhomogeneous random graphs.
We investigate Ising ferrimagnets on square and simple-cubic lattices with exchange couplings between spins of values S=1/2 and S=1 on neighbouring sites and an additional single-site anisotropy term on the S=1 sites. Based mainly on a careful and comprehensive Monte Carlo study, we conclude that there is no tricritical point in the two--dimensional case, in contradiction to mean-field predictions and recent series results. However, evidence for a tricritical point is found in the three-dimensional case. In addition, a line of compensation points is found for the simple-cubic, but not for the square lattice.
We report results of a Wang-Landau study of the random bond square Ising model with nearest- ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic interactions. We consider the case $R=J_{nn}/J_{nnn}=1$ for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent $alpha$. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length $ u$, magnetization $beta$, and magnetic susceptibility $gamma$ increase when compared to the pure model, the ratios $beta/ u$ and $gamma/ u$ remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.
We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local NOT gates. This methodology is well-known in NMR implementations, but previous approaches do not scale efficiently for the general fully-connected Hamiltonian, where the complexity of finding time-optimal solutions makes them only practical up to a few tens of qubits. Given the rapid growth in the number of qubits in cutting-edge quantum processors, it is of interest to investigate the applicability of this control scheme to much larger scale systems with realistic restrictions on connectivity. Here we present an efficient scheme to find near time-optimal solutions that can be applied to engineered qubit arrays with local connectivity for any number of qubits, indicating the potential for practical quantum computing in such systems.
Using the parallel tempering algorithm and GPU accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor(NN) and next-nearest-neighbor(NNN) interactions of the same strength and subject to a uniform magnetic field. Both transitions from the (2x1) and row-shifted (2x2) ordered phases to the paramagnetic phase are continuous. From our data analysis, reentrance behavior of the (2x1) critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on the critical exponents we obtained along the phase boundary, Suzukis weak universality seems to hold.
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