2016, Arnalds, Unnar B., Chico, Jonathan, Stopfel, Henry, Kapaklis, Vassilios, Bärenbold, Oliver, Verschuuren, Marc A., Wolff, Ulrike, Neu, Volker, Bergman, Anders, Hjörvarsson, Björgvin

We present a direct experimental investigation of the thermal ordering in an artificial analogue of an asymmetric two-dimensional Ising system composed of a rectangular array of nano-fabricated magnetostatically interacting islands. During fabrication and below a critical thickness of the magnetic material the islands are thermally fluctuating and thus the system is able to explore its phase space. Above the critical thickness the islands freeze-in resulting in an arrested thermalized state for the array. Determining the magnetic state we demonstrate a genuine artificial two-dimensional Ising system which can be analyzed in the context of nearest neighbor interactions.

2007, Bianchi, Alessandra

We study a continuous time Glauber dynamics reversible with respect to the Ising model on hyperbolic graphs and analyze the effect of boundary conditions on the mixing time. Specifically, we consider the dynamics on an $n$-vertex ball of the hyperbolic graph $H(v,s)$, where $v$ is the number of neighbors of each vertex and $s$ is the number of sides of each face, conditioned on having $(+)$-boundary. If $v>4$, $s>3$ and for all low enough temperatures (phase coexistence region) we prove that the spectral gap of this dynamics is bounded below by a constant independent of $n$. This implies that the mixing time grows at most linearly in $n$, in contrast to the free boundary case where it is polynomial with exponent growing with the inverse temperature $b$. Such a result extends to hyperbolic graphs the work done by Martinelli, Sinclair and Weitz for the analogous system on regular tree graphs, and provides a further example of influence of the boundary condition on the mixing time.