Multicritical dynamics for the ± J Ising Model

Exact dynamical properties are discussed for the ± J Ising model around the multicritical point (MCP). It is found that the relation of relaxations between the non-equilibrium remanent magnetization m(t) and the equilibrium autocorrelation function q(t) at the MCP is different from that at the pure critical point. The dynamic critical exponent for the ferromagnetic ordering defined by m(t)∼t-λm and that for the spin glass ordering defined by q(t)∼t-λq become identical at the MCP. Accurate numerical calculations for them are performed in two and three dimensions using the non-equilibrium relaxation analysis. The MCP is located at pmc=0.8872±0.0008 and the exponent is estimated as λm=λq=0.021±0.001 for the square lattice. They are estimated as pmc=0.7673±0.0003 and λm=λq=0.090±0.003 for the simple cubic lattice. (author)