The reaching of this critical temperature manifests itself with sharp peaks or drops (jumps) among the values of various "observables", or macroscopic thermodynamical quantities, which are directly measurable given a computer simulation of the Ising model; this computer simulation is based on the Monte Carlo technique, and thus relies on random number generation in order to simulate the dynamics of spin flipping in a sample ferromagnet.

Such code decides where and when to flip spins in an initially random spin matrix (can be a 2D or 3D array) following two rules in logical OR:

- Energy of the whole system is lower if this spin is flipped
- A random probability associated with this spin flip is < or = than the negative exponential function of the change in energy and the inverse of the temperature

**Metropolis**algorithm for the acceptance of the spin flip; basically it assumes that a spin gets always flipped if the resulting energy is lower than the starting one.

Ising 2D and 3D models are not that different: 3D model is just an extension of the 2D model code. The XY model is based on the 2D Ising code too, but it relies on a different Hamiltonian for the system.

My code does the following: it is divided into 2 parts,

**Simulation**and

**Data Analysis**.

- Loops for N_beta values of the temperature. At every loop it first initializes the spin system to a
**fixed configuration**, then it runs a MonteCarlo simulation of the system at that temperature. It writes the values of the total Magnetization per site and of the total energy per site into a measurement**file**. - A data analysis program takes the measurement file and computes thermodynamic
**observable**values, writing them to a final**data file**.

__for the CODE:__

**DIRECTIONS**Repeat for each Simulation (run first) and DataAnalysis:

- Set the
**SIDE**of the spin array (I use around 14) - Set the number of sweeps (MonteCarlo iterations, about 40000)
- Set beta_minimum, beta_maximum, N_beta (I use .25, .9,40)
- Compile and Run

https://drive.google.com/file/d/0B36YNo_GwIhxNnZPSVlfTXl2OXc/view?usp=sharing