## Abstract

This paper is concerned with a curious gap in a string of exactly solvable models, a gap that is suggestively related to a completely integrable nonlinear PDE in d = 2 known as Liouville's equation. This PDE emerges in a limit N → ∞ from the equilibrium statistical mechanics of classical point particles with gravitational interactions (SMGI) in dimension d = 2 which, accordingly, is an exactly solvable continuum model in this limit. Interestingly, in d = 1 and all d > 2, the SMGI can be, and partly has been, exactly evaluated for all N ≤ ∞. This entitles one to suspect that the SMGI for d = 2 is likewise exactly solvable for N > ∞, but currently this is an unproven hypothesis. If this conjecture can be answered in the affirmative, spin-offs in various areas associated with Liouville's equation, such as vortex gases, superfluidity, random matrices, and string theory, can be expected.

Original language | English (US) |
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Pages (from-to) | 127-131 |

Number of pages | 5 |

Journal | International Journal of Modern Physics B |

Volume | 11 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 20 1997 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Condensed Matter Physics