Finite-size-scaling study of the simple cubic three-state Potts glass: Possible lower critical dimensiond=3

For small lattices with linear dimension L ranging from L=3 to L=8 we obtain the distribution function P(q) of the overlap q between two real replicas of the three-state Potts-glass model with symmetric nearest-neighbor interaction with a Gaussian distribution. A finite-size-scaling analysis suggests a zero-temperature transition to occur with an exponentially diverging correlation length ${\xi }_{\mathrm{SG}}$∼exp(C/${\mathit{T}}^{\mathrm{\sigma }}$). This implies that d=3 is the lower critical dimension.