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 and that for the spin glass ordering defined by 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 and the exponent is estimated as for the square lattice. They are estimated as and for the simple cubic lattice.
Andrews, Baxter, and Forrester have recently solved two infinite sequences of models that are generalizations of the Ising and hard-square models and exhibit multicriticality. The nature of these new two-dimensional multicritical points is examined in order to determine what universality classes they may represent. Appropriate order parameters are defined and their critical exponents reported. One infinite sequence of multicritical points are continuous melting transitions of $p\ifmmode\times\else\texttimes\fi{}1$ commensurate ordered phases for all integers $p\ensuremath{\ge}2$. The other sequence appears to consist of "generic" multicritical points terminating lines of
n-phase coexistence, again for all integers $n\ensuremath{\ge}2$. The multicritical exponents in this latter sequence coincide with those found by Friedan, Qiu, and Shenker on the basis of assuming conformal invariance and unitarity.