Studies of the Gaussian model

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Abstract
A two-component version of the continuum Gaussian model shows a separation into two fluid phases at high densities. We analyse its behaviour by calculating the cluster integrals and virial coefficients up to 13th order for systems of dimensionality, d, from 2 to 10. We show that there is strong evidence that for d ⩾ 4 the system has a classical critical point but that its behaviour is quite different for d = 2 and 3. The best value of the critical exponent that governs the divergence of the susceptibility, γρ, is 1·55 for d = 3, but a virial expansion to at least 20th order would be needed to give an accurate estimate and our result does not rule out the value of 1·39 that would be expected from a member of the Ising universality class.

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