Abstract
The Landau-de Gennes model of first order transitions is investigated in both Gaussian approximation (GA) and mean field approximation (MFA). “Critical exponents” are calculated. In MFA, the specific heat exponent α’ = 0.5 while in GA, α = 0.5, in agreement with experimental findings in nematic-isotropic (N-I) transitions of liquid crystals. However, in GA, the exponents on the two sides of Tc, are not equal to each other in general. For example, α = 0.5 ≠ α’, γ = 1 ≠ γ’ and υ = 0.5 ≠ υ’ The tricritical-point hypothesis of the N-I transition is discussed in relation to our results. Throughout this work, the similarities and differences between first and second order phase transitions are emphasized. Scaling law results from second order transitions cannot be simply applied in first order transitions.
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