2D Ising Model (analytical expressions)

[Orion_PKFD]

Hi all,

I am doing a program to simulate the 2D Ising Model under the metropolis algorithm. In order to check my results I would like to compare them with the analytical expressions for the mean energy, magnetization, specific heat and magnetic susceptibility.

I already found the expressions for the mean energy, magnetization and specific heat. However, when I plot the expression for the mean energy the result does not look right. I used the one in Huang's book. Concerning the magnetic susceptibility, I couldn't find any analytical expression...

Anyone could give me some help? Thanks.

Best regards!

 

[LightHero]

</code>The analytical expression for the mean energy of the 2D Ising Model is given by:E = -J * N * M^2, where N is the number of spins in the lattice and M is the average magnetization. This can be derived from the Hamiltonian of the Ising Model, which is given by: H = - J * sum(s_i * s_j), where J is the coupling constant and s_i and s_j are the spin values of two neighbouring sites.The analytical expression for the magnetization of the 2D Ising Model is given by:M = (1/N) * sum(s_i) where N is the number of spins in the lattice and s_i is the spin value of a particular site. This can be derived from the Hamiltonian of the Ising Model, which is given by: H = - J * sum(s_i * s_j), where J is the coupling constant and s_i and s_j are the spin values of two neighbouring sites.The analytical expression for the specific heat of the 2D Ising Model is given by:C = (k_B / T^2) * var(E) where k_B is Boltzmann's constant, T is the temperature, and E is the mean energy. This can be derived from the Hamiltonian of the Ising Model, which is given by: H = - J * sum(s_i * s_j), where J is the coupling constant and s_i and s_j are the spin values of two neighbouring sites.Finally, the analytical expression for the magnetic susceptibility of the 2D Ising Model is given by:X = (1/T) * var(M) where T is the temperature and M is the average magnetization. This can be derived from the Hamiltonian of the Ising Model, which is given by: H = - J * sum(s_i * s_j), where J is the coupling constant and s_i and s_j are the spin values of two neighbouring sites.