Phase transition of a colloidal suspension in the vicinity of a fluctuating membrane using the lattice gas model

This investigation aims to study the phase transition of colloidal particles near a fluctuating membrane using the lattice gas model. The first step is to derive a new Ising-like Hamiltonian. We addressed this problem in the continuous limit by applying the Hubbard–Stratonovich transformation. The values predicted by the mean-field approximation, or its generalization namely, the Landau approximation are α ′ + = α ′ − = 0 , β ′ = 1 / 2 , γ + = γ − = 1 , δ = 3 , η = 0 and ν = 1 / 2 . We have also established scaling relations between these critical exponents. The gas-on-network model was employed to demonstrate the hysteresis phenomenon, providing a quantitative description at the microscopic scale of the phase transition in the colloidal suspension , from the ordered phase to the disordered phase. In comparison with recent studies, the lattice gas model remains a valuable tool and promising for describing the organization of colloidal particles near a soft interface. • Determining the Ising Hamiltonian-like. • Phase transition of the colloid suspension near a fluctuating membrane using the lattice gas model. • Using the Hubbard–Stratonovich transformation. • Critical behavior has been shown, with universal critical exponent. • Hysteresis phenomenon.