_{n}/2-\mu )}{2},\qquad \Delta _{n}=(e^{\beta
(\epsilon _{n}/2-\mu )}+1)^{-1}  \eqnum{3.7}$$

The leading contributions of the one-loop polarization operator coefficients (3.7) at low temperatures $\left( T\ll \omega _{c}\right) $ are

$${\it \Pi }_{{\it 0}}=\frac{2\beta \overline{b}}{\pi }e^{-\beta \overline{b}%
/2m},\qquad {\it \Pi }_{{\it 0}}\,^{\prime }=\frac{mN}{2\pi \overline{b}}%
{\it \Lambda },\qquad {\it \Pi }_{{\it 1}}=\frac{N}{2\pi }{\it \Lambda }%
,\quad {\it \Pi }_{\,{\it 2}}=\frac{N^{2}}{4\pi m}{\it \Lambda },\qquad {\it %
\Lambda }=\left[ 1-\frac{2\beta \overline{b}}{m}e^{-\beta \overline{b}%
/2m}\right]  \eqnum{3.8}$$

and at high temperatures $\left( T\gg \omega _{c}\right) $ are

$${\it \Pi }_{{\it 0}}=\frac{m}{2\pi }\left[ \tanh \frac{\beta \mu }{2}%
+1\right] ,\qquad {\it \Pi }_{{\it 0}}\,^{\prime }=-\frac{\beta }{48\pi }%
%TCIMACRO{\func{sech} }
%BeginExpansion
\mathop{\rm sech}%
%EndExpansion
\!^{2}\!\,\left( \frac{\beta \mu }{2}\right) ,\qquad {\it \Pi }_{{\it 1}}=%
\frac{\overline{b}}{m}{\it \Pi }_{{\it 0}}\,^{\prime },\qquad {\it \Pi }_{\,%
{\it 2}}=\frac{1}{12m^{2}}{\it \Pi }_{{\it 0}}  \eqnum{3.9}$$

In these expressions $\mu $ is the chemical potential and $m=2m_{e}$ ($m_{e}$ is the electron mass). These results are in agreement with those found in refs.[@8],[@14].

MCS Linear Equations
--------------------

To find the response of the anyon fluid to an externally applied magnetic field, one needs to use the extremum equations derived from the effective action (3.1). This formulation is known in the literature as the self-consistent field approximation[@11]. In solving these equations we confine 