"The Ising Model for Calculation Energy and Magnetization in Magnetic Fields (B=0, B≠0) for different Lattice Sizes"

Abstract

"Two dimensional Ising model's partial transition location has been determined with significant samples using Monte Carlo method. The magnetization per site (µ) and the energy per site (j),heat capacity (CV), susceptibility (x)of a ferromagnetic substance are calculated as a function of inverse temperature (βJ) for different lattice sizes, in magnetic fields (B=0,B≠0). The critical inverse temperature (βC=0.435 KB/J) has been determined. The precise partition functions (i.e. precise solutions) of the Ising model in (L×L= 4, 8, 16, 32) the square lattice sizes with free boarders stipulations are acquired after categorize all 2L×L=216×16 (≈1.157×1077) and 232×32 (≈1.79×10308) shapes of spin and we observe how the system evolves across steps to achieve balance. Moreover, the stage of transitions and critical conditions have been discussed using the precise partition function in (L×L=16, 32) square lattice sizes with free boarders stipulations. "