# Needed Clarification: In Calculation of specific heat of Ising model (Simulation)

I am want to calculate the specific heat for 2D 100x100 square lattice ising model. I have calculated the correlation time, viz., $$\tau$$. Now I want to calculate the specific heat and error in specific heat using the Jackknife method. Following are the steps which I am following, I want to know that I am going in right direction.

1. I have arrays of Energy for each temperature for a particular Monte Carlo step. (1 Monte Carlo step = 1 iteration). I will divide the set of energies into $$n=\frac{t_{MAX}}{2\tau}$$, where $$t_{MAX}$$ is total number of Monte Carlo steps.

2. Each divided set of energies contains $$2\tau$$ number of energies. For each set we calculate the variance, multiplying variance with $$\beta^2$$ gives specific heat for that set which we call $$c_i$$.

3. Now, we use the Jackknife method: discarding $$n^{th}$$ measurement, we calculate $$\overline c_{n_{JK}}$$: $$\overline{c}_{n_{JK}}=\frac{1}{n-1}\sum_{i\ne n}c_i$$

4. We calculate specific heat as average if $$\{\overline{c}_{n_{JK}}\}$$, viz., $$\overline c_{JK}$$: $$\overline{c}_{JK}=\frac{1}{n}\sum_{i=1}^N\overline{c}_{i_{JK}}$$

5. Now comes the error estimation, which is given by square root of the Jackknfe varience : $$\sigma^2_{JK}=\frac{n-1}{n}\sum_{i=1}^{N}(\overline{c}_{JK}-\overline{c}_{i_{JK}})^2$$ For large $$n$$ the error is simply: $$\sigma_{JK}=\sqrt{\sum_{i=1}^{N}(\overline{c}_{JK}-\overline{c}_{i_{JK}})^2}$$

Is this that all correct?

PS: I do not know if we are allowed to ask a question for clarification on physics stack exchange. I hope this is not against the physics stack exchange policy.

1. In your point 1, After system has reached Equilibrium, viz., after $$\tau$$, you need to take uncorrelated energies, i.e., energies after every 2$$\tau$$. In short, you take energies at $$\tau, 3\tau, 5\tau, \dots$$ and discard others.
2. If you calculate variance of new set of energies at $$\tau, 3\tau, 5\tau, \dots$$ and multiply by $$\beta^2$$, you will get specific heat.
3. Calculate $$c_n$$ which is, variance of all Energy excluding energy at n-th index.