Dynamical frustration in ANNNI model and annealing

Zero temperature quench in the Axial Next Nearest Neighbour Ising (ANNNI) model fails to bring it to its ground state for a certain range of values of the frustration parameter $\kappa$, the ratio of the next nearest neighbour antiferromagnetic interaction strength to the nearest neighbour one. We apply several annealing methods, both classical and quantum, and observe that the behaviour of the residual energy and the order parameter depends on the value of $\kappa$ strongly. Classical or thermal annealing is found to be adequate for small values of $\kappa$. However, neither classical nor quantum annealing is effective at values of $\kappa$ close to the fully frustrated point $\kappa=0.5$, where the residual energy shows a very slow algebraic decay with the number of MCS.Comment: 6 pages,10 figures, to be published in Proceedings of " The International Workshop on Quantum annealing and other Optimization Methods

Ising model in small-world networks

The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the thermodynamic limit, the phase transition has a mean-field character for any finite value of the rewiring probability p, which measures the disorder strength of a given network. For small values of p, both the transition temperature and critical energy change with p as a power law. In the limit p -> 0, the heat capacity at the transition temperature diverges logarithmically in two-dimensional (2D) networks and as a power law in 3D.Comment: 6 pages, 7 figure