the confinement of the system to a bounded region (a condition which is closer to the experimental situation than the free-space case) is crucial for the realization of the Meissner effect inside the charged anyon fluid at finite temperature.

Let us investigate the linear response of a charged anyon fluid at finite temperature and density to an externally applied magnetic field in the specific case of an infinite-strip sample. The linear response of the medium can be found under the assumption that the quantum fluctuations of the gauge fields about the ground-state are small. In this case the one-loop fermion contribution to the effective action, obtained after integrating out the fermion fields, can be evaluated up to second order in the gauge fields. The effective action of the theory within this linear approximation [@8],[@11] takes the form

$$\Gamma _{eff}\,\left( A_{\nu },a_{\nu }\right) =\int dx\left( -\frac{1}{4}%
F_{\mu \nu }^{2}-\frac{N}{4\pi }\varepsilon ^{\mu \nu \rho }a_{\mu }\partial
_{\nu }a_{\rho }+en_{e}A_{0}\right) +\Gamma ^{\left( 2\right) }  \eqnum{3.1}$$

$$\Gamma ^{\left( 2\right) }=\int dx\Pi ^{\nu }\left( x\right) \left[ a_{\nu
}\left( x\right) +eA_{\nu }\left( x\right) \right] +\int dxdy\left[ a_{\nu
}\left( x\right) +eA_{\nu }\left( x\right) \right] \Pi ^{\mu \nu }\left(
x,y\right) \left[ a_{\nu }\left( y\right) +eA_{\nu }\left( y\right) \right]$$ 