Project 4: Difference between revisions
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<math> E = - J \sum_{\langle i,j \rangle} S_i S_j - H \sum_i S_i </math> | <math> E = - J \sum_{\langle i,j \rangle} S_i S_j - H \sum_i S_i </math> | ||
where <math> \langle i,j \rangle </math> means that the sum runs over all pairs of nearest neighbor spins (attached to the lattice sites), and <math> J </math> is the exchange coupling. Positive <math> J >0 </math> interaction between the spins leads to ferromagnetism, will negative <math> J >0 </math> gives rise to antiferromagnetism in the Ising model. Choose units so that <math> |J|=1 </math> and the Boltzmann constant is <math> k_B=1 </math>. The free parameters of the model are then just the temperature <math> T </math> and the applied field <math> H </math>. | |||
Parth I | |||
Revision as of 14:13, 2 April 2012
First and second order phase transition in the Ising model of ferromagnetism
Write a program for the 2D Ising model on a square lattice with periodic boundary conditions which is placed in an applied external magnetic field . The energy of a particular state of the system is given by:
where means that the sum runs over all pairs of nearest neighbor spins (attached to the lattice sites), and is the exchange coupling. Positive interaction between the spins leads to ferromagnetism, will negative gives rise to antiferromagnetism in the Ising model. Choose units so that and the Boltzmann constant is . The free parameters of the model are then just the temperature and the applied field .
Parth I
