The derivative of the natural logarithm of this expression with respect to beta gives the expected value for the energy.
According to the Lee-Yang theorem, in the Ising model this expression has all imaginary zeros. Peirels showed that the logarithm of this expression is not analytic at a phase transition. This expression is equal to the trace of the transfer matrix. The derivative of the natural logarithm of this expression with respect to beta gives the expected value for the energy. This expression is used to normalize the probability of a particular state, and it can be used to calculate the free energy of a (*) canonical ensemble. The natural log of it times negative kT gives the Helmholtz free energy. It is equal to the sum over all Boltzmann factors, or the sum of the function e to the negative beta times energy summed over all microstates. For 10 points, name this value from statistical mechanics symbolized Z.
According to the Lee-Yang theorem, in the Ising model this expression has all imaginary zeros.
partition function [or Z before mention]