A Lattice Model of Liquid Helium, I

A lattice model is proposed in order to explain the peculiar properties of liquid helium II. In the present model, liquid is regarded as a lattice composed of atoms and holes. Each atom can migrate by exchanging its position with an adjacent hole if the latter exists. In terms of operators which create or annihilate an atom at each lattice point, the kinetic and potential energies are defined so as to have a correct form in the limit of vanishing lattice spacing. Then it is proved that the grand partition function of our lattice liquid is equal to the partition function of a system of vector spins subjected to an external magnetic field, provided a proper identification is made between corresponding quantities of both systems. Various approximation methods used in the problem of ferromagnets are appliciable and enable us to attain the results which explain most of the characteristic features of liquid helium.

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