Statistical Mechanics of the Biomembrane Phase Transition in Its Relation with Quantum Mechanical Problem of Hard Core Bosons in Two Dimensions

概要

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Statistical mechanics of the gel-phase to fluid-phase transition of the lipid bilayer is described by the extended modified dimer model including the lateral expansion of the dimer lattice. The free energy of the dimer lattice is obtained from the ground state energy of the hard core bosons placed on the two-dimensional square lattice. Fisher's scaling argument on the free energy is shown to be equivalent to the binary collision approximation for the many boson problem. In the low density limit the ρ^2 term of the free energy is replaced by ρ^2/ln(1/ρ). From this result, it is concluded that the extended model always exhibits the first order phase transition. It is pointed out that the logarithmic reduction appears only for very small values of ρ, and hence is irrelevant to the real biomembrane problem. The fermion approximation used in our previous papers leads to much lower (or better) free energy than that obtained from the binary collision approximation.
理論物理学刊行会の論文
1985-03-31