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Topological Expansion in the Complex Cubic Log–Gas Model: One-Cut Case

2016
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Journal of statistical physics
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We prove the topological expansion for the cubic log-gas partition function \[ Z_N(t)= \int_\Gamma\cdots\int_\Gamma\prod_{1\leq j<k\leq N}(z_j-z_k)^2 \prod_{k=1}^Ne^{-N\left(-\frac{z^3}{3}+tz\right)}\mathrm dz_1\cdots \mathrm dz_N, \] where $t$ is a complex parameter and $\Gamma$ is an unbounded contour on the complex plane extending from $e^{\pi \mathrm i}\infty$ to $e^{\pi \mathrm i/3}\infty$. The complex cubic log-gas model exhibits two phase regions on the complex $t$-plane, with one cut

doi:10.1007/s10955-016-1621-x
fatcat:yl6aw3usivhalerymk6u2v4dny