Round 12: Tossup 10

Gibbons and Hawking found this quantity could be approximated using an Euclidean saddle point of a path integral over spacetime geometries. This quantity must have imaginary zeroes in ferromagnetic spin lattices per the Lee-Yang theorem. In the Sherrington-Kirkpatrick model, the average of the log of this quantity is set equal to the limit (15[1])as n approaches zero of “this quantity to the n [pause] minus one [pause] all over n” in the canonical example of the (*) replica trick. The expectation value of total energy equals negative the derivative of the natural log of this quantity with respect to beta. This quantity equals the sum over all microstates of e to the negative beta times energy, making it the sum of all Boltzmann factors. For 10 points, the Boltzmann distribution is normalized by what thermodynamic quantity, symbolized Z? ■END■

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