Title: The Energy Density in the Toric Ising Model

Abstract: 
I calculate rigorously the scaling limit of energy density of the 
critical Ising model on the square lattice on the two dimensional torus. 
An exact formula is found for the energy density scaling limit asymptotics 
and thus calculations that have appeared in physics literature are validated. 
We also demonstrate how the energy density of the discrete Ising model is 
related to determinants of certain discrete Laplacians, and in the process 
of our calculation, we also find the scaling limit of the Ising model 
partition function.