  It is found that noncommutative U(1) gauge field on the fuzzy sphere S^2_N is
equivalent in the quantum theory to a commutative 2-dimensional U(N) gauge
field on a lattice with two plaquettes in the axial gauge A_1=0. This quantum
equivalence holds in the fuzzy sphere-weak coupling phase in the limit of
infinite mass of the scalar normal component of the gauge field. The doubling
of plaquettes is a natural consequence of the model and it is reminiscent of
the usual doubling of points in Connes standard model. In the continuum large N
limit the plaquette variable W approaches the identity 1_{2N} and as a
consequence the model reduces to a simple matrix model which can be easily
solved. We compute the one-plaquette critical point and show that it agrees
with the observed value \bar{\alpha}_*=3.35. We compute the quantum effective
potential and the specific heat for U(1) gauge field on the fuzzy sphere
S^2_{N} in the 1/N expansion using this one-plaquette model. In particular the
specific heat per one degree of freedom was found to be equal to 1 in the fuzzy
sphere-weak coupling phase of the gauge field which agrees with the observed
value 1 seen in Monte Carlo simulation. This value of 1 comes precisely because
we have 2 plaquettes approximating the NC U(1) gauge field on the fuzzy sphere.

High Energy Physics - Theory