Numerical study of competing spin-glass and ferromagnetic order

Abstract

Two-and three-dimensional random Ising models with a Gaussian distribution of couplings with variance J and nonvanishing mean value J 0 are studied using the zero-temperature domain-wall renormalization group ͑DWRG͒. The DWRG trajectories in the (J 0 ,J) plane after rescaling can be collapsed on two curves: one for J 0 /JϾr c and the other for J 0 /JϽr c . In the first case the DWRG flows are toward the ferromagnetic fixed point both in two and three dimensions while in the second case flows are towards a paramagnetic fixed point and spin-glass fixed point in two and three dimensions, respectively.

Giant Shapiro steps for two-dimensional Josephson-junction arrays with time-dependent Ginzburg-Landau dynamics

“…In the FTBC case the translational symmetry of the ground state is automatically preserved and consequently this boundary condition directly yields the correct result. We also calculated the critical current with the busbar geometry 18 and obtained an even smaller value of I c (f = 1/2) than for the conventional uniform injection method, as was already noticed in Refs. 5 and 24.…”

Spin-Glass-like Behavior in the Selenide Cr2Sn3Se7

“…Because the nn interactions are ferro-rather than antiferromagnetic, the presence of triangular M motifs may not be said to lead to topological frustration in the present case. On the other hand, the phenomena observed herein might be related to a model system in which ferromagnetic order competes with spin glass behavior and a percolation threshold exists (1,18).…”

Domain wall renormalization group study of theXYmodel with quenched random phase shifts

“…To our knowledge, for the systems of interest no algorithm exists which can locate the global energy minima in polynomial time. We are left with two methods: (i) repeated simple quenches from an arbitrary initial configuration to T = 0 followed by a downward slide to the nearest local minimum and (ii) simulated annealing 34 which is considerably more efficient 35 . By this we mean that, for the same CPU time, simulated annealing finds a lower energy than simple quenching.…”

“…To our knowledge, there is no algorithm applicable to the systems of interest which will find exact minima in polynomial time, such as the branch and cut algorithm 32 for the 2D Ising spin glass or numerically exact combinatorial optimization algorithms 33 for gauge and vortex glass models in the infinite screening limit, so we have to live with the fact that our problem is NP complete and the required CPU time explodes as L increases. We use simulated annealing 34,35 to estimate the lowest energies, which seems considerably more efficient than simple quenching to T = 0, but we are unable to go beyond L = 7 in 3D and L = 10 in 2D. We wish to extract the stiffness exponent θ from the scaling ansatz of Eq.…”