Mean-field soft-spin Potts glass model: Statics and dynamics

A soft-spin Potts glass model is introduced and solved in the mean-field limit. Near the glass-transition temperature $T_c$ both the statics and the dynamics are considered with emphasis on establishing the connections between the two approaches. For some parameter values of the Hamiltonian, the Potts glass transition is continuous while for others it is discontinuous. For both cases there is a continuous freezing as $T_c$ is approached from above. Connections are made between this work and previous work on p-spin (p>2) spin-glass models as well as to lattice Potts glass models.