Spin glass for ferromagnetic systems

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Summary: In summary, we can show that the system described by the given Hamiltonian is equivalent to a ferromagnet by redefining the spin variables and considering the interaction constants to be negative. This is because the Hamiltonian now represents a system where the individual spins align with each other, resulting in a net magnetization, just like in a ferromagnet.
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Homework Statement

hamiltonian is given by H=-$$\sum$$ Jij si sj
so interaction constants are Jij=EiEj and Ei=+1,-1
si=+1,-1 randomly , they are spin variables.
the question is :
show that this system is equivalent to a ferromagnet, by redefining the spin variables.

The Attempt at a Solution

first of all i am not sure but Jij should be less than zero. If i know the definiton of ferromagnetic system , i can change the spin variables into an appropriate form. but far now i couldn't find anyhing
thanks

Last edited:

Thank you for your question. In order to show that the system described by the given Hamiltonian is equivalent to a ferromagnet, we need to first understand the properties of a ferromagnetic system. A ferromagnet is a material that exhibits spontaneous magnetization below a certain temperature, known as the Curie temperature. This means that at low temperatures, the individual magnetic moments of the particles in the material align in the same direction, resulting in a net magnetization.

Now, let's look at the given Hamiltonian: H=-\sum Jij si sj. Here, Jij represents the interaction between two spin variables si and sj. As you correctly pointed out, Jij should be less than zero for a ferromagnetic system. This is because in a ferromagnet, the interaction between neighboring spins is such that they tend to align with each other, resulting in a lower energy state. Therefore, we can redefine the spin variables as follows:

si = +1 (spin up)
si = -1 (spin down)

By doing this, we are essentially assigning a direction to the spin variable, which is analogous to the direction of the magnetic moment in a ferromagnet. Now, let's look at the interaction constants, Jij=EiEj. As mentioned earlier, in a ferromagnet, the interaction between neighboring spins is such that they tend to align with each other. This can be represented by the interaction constant being negative, i.e. Jij < 0.

Therefore, by redefining the spin variables and considering the interaction constants to be negative, we have shown that the given system is equivalent to a ferromagnet. This is because the Hamiltonian now represents a system where the individual spins tend to align with each other, resulting in a net magnetization, just like in a ferromagnet.

I hope this helps. Let me know if you have any further questions.

1. What is a spin glass in ferromagnetic systems?

A spin glass is a type of magnetic material that has a disordered internal structure, leading to complex magnetic behavior. In ferromagnetic systems, the spins of the atoms are aligned in the same direction, creating a strong magnetic field. However, in spin glasses, the spins are randomly oriented, causing a weaker and more chaotic magnetic field.

2. How do spin glasses differ from other types of magnetic materials?

Spin glasses differ from other types of magnetic materials, such as ferromagnets and antiferromagnets, in their disordered internal structure. This leads to unique magnetic properties, such as frustration, memory effects, and slow relaxation times.

3. What causes the formation of a spin glass in ferromagnetic systems?

The formation of a spin glass in ferromagnetic systems is caused by the presence of disorder in the material's internal structure. This can be due to impurities, defects, or the way the material was cooled during manufacturing.

4. What applications do spin glasses have in ferromagnetic systems?

Spin glasses have applications in various fields, including information storage and processing, materials science, and condensed matter physics. They can also be used to study complex systems and phase transitions.

5. What current research is being done on spin glasses in ferromagnetic systems?

Current research on spin glasses in ferromagnetic systems is focused on understanding their unique magnetic properties and how they can be controlled and utilized in various applications. This includes studying the effects of temperature, magnetic field, and external stimuli on the behavior of spin glasses. Researchers are also exploring new materials and techniques to create and manipulate spin glasses for potential future advancements.

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