Temperature estimation in the two-dimensional Ising model
We present two new algorithms for the estimation of the temperature from a realization of a 2-D Ising model. The methods here introduced are based in the maximization of pseudo likelihood and on the minimum mean squared error (MSE) fit of the conditional probability function. We derive the analytical expressions of these estimators and also we include computational results comparing these new techniques with the traditional method. A very good performance in terms of the average absolute error and the average standard deviation is demonstrated through simulations in a 100 x 100 lattice in the ferromagnetic and anti ferromagnetic cases. Summarizing, we have provided two new useful computational tools that allow us to measure the "virtual" temperature of an Ising like system.
ising model mean squared error ferromagnet