Laboratoire de Physique Théorique

de la Matière Condensée

Ramgopal Agrawal (LPTHE)

Critical dynamics of the \(\pm J\) Ising model

The \(\pm J\) Ising model is a simple frustrated spin model, where the exchange couplings independently take the discrete value \(-J\) with probability \(p\) and \(+J\) with probability \(1-p\). Here, we investigate the nonequilibrium critical behavior of the bi-dimensional \(\pm J\) Ising model, after a quench from different initial conditions to a critical point T_c(p) on the paramagnetic-ferromagnetic (PF) transition line, especially, above, below and at the multicritical Nishimori point (NP). The dynamical critical exponent \(z_c\) seems to exhibit non-universal behavior for quenches above and below the NP, which is identified as a pre-asymptotic feature due to the repulsive fixed point at the NP. Whereas, for a quench directly to the NP, the dynamics reaches the asymptotic regime with \(z_c \simeq 6.02(6)\). We also consider the geometrical spin clusters (of like spin signs) during the critical dynamics. Each universality class on the PF line is uniquely characterized by the stochastic Loewner evolution (SLE) with corresponding parameter \(\kappa\).