Casimir-Like Effect from Thermal Field Fluctuations

Landau-Ginzburg $\phi^4$ field theory is usually applied to systems for understanding continuous phase transitions at critical points. Here we analyze the thermal using a similar free energy description from statistical perspective, and study fluctuations in such with particular focus on realizing Casimir effect. Initially, qualitatively describe emergence of Casimir-like effect mean-field approximation further derive it coarse-graining perturbative renormalization procedure vicinity Gaussian-fixed point. These results may lead scalar fields without employing concept zero-point cosmological sense.