The expected value for the energy of a system is the negative partial derivative of its (*) log with respect to 1 over k T. Its reciprocal often appears as a normalization factor, such as in the probability of a microstate.
If this quantity is a finite polynomial in the activity, z, its zeroes on the complex z plane only occur as conjugate pairs or for negative, real z, so there is a singularity or branch cut for positive, real z as shown by Lee and Yang. It can be found by taking the Laplace transform of the density of states or the trace of the density matrix. Each quadratic degree of freedom in a system's Hamiltonian contributes root pi k T over a constant to this quantity. The expected value for the energy of a system is the negative partial derivative of its (*) log with respect to 1 over k T. Its reciprocal often appears as a normalization factor, such as in the probability of a microstate. For 10 points, name this function from statistical mechanics that is symbolized Z and can be used to find most of the macroscopic properties of a system.
If this quantity is a finite polynomial in the activity, z, its zeroes on the complex z plane only occur as conjugate pairs or for negative, real z, so there is a singularity or branch cut for positive, real z as shown by Lee and Yang.
grand partition function [or Z until it is read; prompt on Q, xi, Y]