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cosmicraga
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In the well known Ising model, without any external field (H=0), the energy (E), spins (s) and exchange interaction (J) are related as in the following equation
$$
E = -\sum_{<ij>}J_{ij}s_{i}s_{j}
$$
Jij is site dependent and consists of three components JAA, JBB and JABwhere A is say up spin and B is down spin on a lattice (say SL).
For a material of type AxB1-x with system size N = 100 (N is number of spins), I know the values of JAA, JBB and JAB. Here JAA=E(x=1)/nAA and JBB=E(x=0)/nBB are constant for any x. JAB changes with x. nAA is number of AA bonds.
E(x=1) means Energy of the system when x=1 for AxB1-x material, i.e. Energy of the system when the system consists of only up spins (all A). Similarly E(x=0) means energy of the system when there is only down spins (all B).
x is composition, x=0.25 means 25% of N is A spins and rest are B spins.
**Queston 1**: If I increase my system size N to 200, then shall the values of JAA, JBB and JAB change?
**Question 2**: If the values of JAA, JBB and JAB change with N, then with what factor shall I increase it?
$$
E = -\sum_{<ij>}J_{ij}s_{i}s_{j}
$$
Jij is site dependent and consists of three components JAA, JBB and JABwhere A is say up spin and B is down spin on a lattice (say SL).
For a material of type AxB1-x with system size N = 100 (N is number of spins), I know the values of JAA, JBB and JAB. Here JAA=E(x=1)/nAA and JBB=E(x=0)/nBB are constant for any x. JAB changes with x. nAA is number of AA bonds.
E(x=1) means Energy of the system when x=1 for AxB1-x material, i.e. Energy of the system when the system consists of only up spins (all A). Similarly E(x=0) means energy of the system when there is only down spins (all B).
x is composition, x=0.25 means 25% of N is A spins and rest are B spins.
**Queston 1**: If I increase my system size N to 200, then shall the values of JAA, JBB and JAB change?
**Question 2**: If the values of JAA, JBB and JAB change with N, then with what factor shall I increase it?
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