  We study a two-dimensional spin model obtained by "Higgsing" the rank-2 U(1)
lattice gauge theory (LGT) with scalar or vector charges on the L_x * L_y
square lattice under the periodic boundary condition (PBC). There are p degrees
of freedom per orbital and three orbitals per unit cell in the spin model. The
resulting spin model is a stabilizer code consisting of three mutually
commuting projectors that are, in turn, obtained by Higgsing the mutually
commuting Gauss's law operators and the magnetic field operators in the
underlying LGT. The spin model thus obtained is exactly solvable, with the
ground state degeneracy (GSD) D given by log_p D=2+(1+delta_{L_x mod
p,0})(1+delta_{L_y mod p,0}) when p is a prime number. Two types of dipole
excitations, pristine and emergent, are identified. Both the monopoles and the
dipoles are free to move, with restrictions on monopoles to hop only by p
lattice spacing along with certain directions. The monopole-monopole braiding
phase depends on the separation of the x or y coordinates of the initial
monopole positions, making it distinct from the ordinary anyon braiding
statistics. The monopole-dipole braiding obeys the usual anyonic statistics.
Despite the oddity, the monopole-monopole braiding phase can be understood as
the Aharonov-Bohm phase of some emergent vector potentials.
