- #1

Marioweee

- 18

- 5

- Homework Statement
- See below

- Relevant Equations
- See below

We have a set of N spins arranged in one dimension that can take the values $$s_i=\pm 1$$. The Hamiltonian of the system is:

$$H=-\frac{J}{2N}\sum_{i \neq j}^{N} s_i s_j -B\sum_{i=1}^{N}s_i.$$

where $$J>0$$, B is an external magnetic field, and the first sum runs through all the values of i and j between 1 and N different from each other.

To analyze the behavior of the system, the most interisting observable is spin magnetization, whose definition is:

$$m\equiv \frac {1}{N}\sum_{i}^{N} si, \; \; m\in [-1,1].$$

Deduces the E(m) energy of a configuration $${s_i}_{i=1}^N$$ as a function of its magnetization by

spin. Find the minimum energy configurations.

Well, the truth is that I do not know very well how to answer the question that is asked. I have already solved the problem in the case that there is no interaction between spins. The problem is that I am not familiar with non-ideal Hamiltonians, that is, that there is interaction between the particles that make up the system. In addition, I am puzzled by the fact that I am asked to obtain the energy as a function of spin magnetization, since this leads me to think that it is not necessary to determine the partition function to solve this question. Thank you very much for reading and for the help.

$$H=-\frac{J}{2N}\sum_{i \neq j}^{N} s_i s_j -B\sum_{i=1}^{N}s_i.$$

where $$J>0$$, B is an external magnetic field, and the first sum runs through all the values of i and j between 1 and N different from each other.

To analyze the behavior of the system, the most interisting observable is spin magnetization, whose definition is:

$$m\equiv \frac {1}{N}\sum_{i}^{N} si, \; \; m\in [-1,1].$$

Deduces the E(m) energy of a configuration $${s_i}_{i=1}^N$$ as a function of its magnetization by

spin. Find the minimum energy configurations.

Well, the truth is that I do not know very well how to answer the question that is asked. I have already solved the problem in the case that there is no interaction between spins. The problem is that I am not familiar with non-ideal Hamiltonians, that is, that there is interaction between the particles that make up the system. In addition, I am puzzled by the fact that I am asked to obtain the energy as a function of spin magnetization, since this leads me to think that it is not necessary to determine the partition function to solve this question. Thank you very much for reading and for the help.