Nonequilibrium critical dynamics of the two-dimensional $\pm J$ Ising model

Abstract

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 $1-p$. It is especially appealing due to its connection to quantum error correcting codes. Here, we investigate the nonequilibrium critical behavior of the two-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 $\kappa$. Moreover, for the critical quenches from the paramagnetic phase, the model, irrespective of the frustration, exhibits an emergent critical percolation topology at the large length scales.

29 pages, 11 figures

References in corpus (12)

• Error Threshold for Color Codes and Random 3-Body Ising Models
• Exact results for curvature-driven coarsening in two dimensions
• Locations of multicritical points for spin glasses on regular lattices
• Winding angle variance of Fortuin-Kasteleyn contours
• Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Strong disorder fixed points in the two-dimensional random-bond Ising model
• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
• Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures
• Coarsening and percolation in a disordered ferromagnet
• Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
• Asymptotic States of Ising Ferromagnets with Long-range Interactions

Cited by in corpus (4)

• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Critical clusters in liquid crystals: Fractal geometry and conformal invariance
• Dynamical critical behavior on the Nishimori point of frustrated Ising models
• Lack of self-averaging of the critical internal energy in a weakly-disordered Baxter model