A one-dimensional lattice gas with long-range many-body interactions is studied by a matrix method for the model of the transition between native and denatured states of globular proteins. The interactions in our model have the nature that two particles situated on two different sites can interact with each other only when all sites between them are occupied by other particles, or in other words, only when they are in a same island which is formed by particles situated side by side. In this system a phase transition occurs in the limit of the infinite long-range interaction and under certain potential functions. The sharpness and the all-or-none type property of the transitions are discussed from the nature of interaction.
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