Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration

We study numerically a two-dimensional random-bond Ising model where frustration can be tuned by varying the fraction $a$ of antiferromagnetic coupling constants. At low temperatures the model exhibits a phase with ferromagnetic order for sufficiently small values of $a$, $a<a_f$. In an intermediate range $a_f<a<a_a$ the system is paramagnetic, with spin glass order expected right at zero temperature. For even larger values $a>a_a$ an antiferromagnetic phase exists. After a deep quench from high temperatures, slow evolution is observed for any value of $a$. We show that different amounts of frustration, tuned by $a$, affect the dynamical properties in a highly non trivial way. In particular, the kinetics is logarithmically slow in phases with ferromagnetic or antiferromagnetic order, whereas evolution is faster, i.e. algebraic, when spin glass order is prevailing. An interpretation is given in terms of the different nature of phase space.