Statistical physics and magnetization

In summary, the conversation discusses a system of three aligned spins with couplings between first neighbors and a magnetic moment of ## \vec{\mu} = s \mu \vec{S}##. The system is in a thermal equilibrium and a field ## H= H\vec{u_z}##. The hamiltonian is given as ##H=J[S(1)S(2)+S(2)S(3)] -2\mu H[S_z(1) + S_z(2)+S_z(3)]##. The conversation then moves on to discussing the calculation of possible microscopic states and their energy, internal energy and entropy, partition function, and magnetization. The process of calculating the partition function involves
  • #1
PhoenixWright
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Homework Statement



Consider a system of three aligned spins with S=1/2. There are couplings between first neighbors. Each spin has a magnetic moment ## \vec{\mu} = s \mu \vec{S}##. The system is in a field ## H= H\vec{u_z}## at thermal equilibrium. The hamiltonian is:
##H=J[S(1)S(2)+S(2)S(3)] -2\mu H[S_z(1) + S_z(2)+S_z(3)]##
So, we want to calculate:
a) Possible microscopic states and their energy.
b) Internal energy U(T,H) and entropy S(T,H), for 1) T=0, H=0; 2) H=0, J <<kT
c) Partition function in closed form
d) Magnetization M(T,H).

Homework Equations


Below:

The Attempt at a Solution


I have been searching, and I think this is a 1-dimensional problem of the Ising model, but I am not sure, and I have no idea how I should start.
I know that the microscopic states of the system are 8, because there are two spin orientations (so, 2x2x2=8). But, how can I calculate the partition function?
Actually, they ask me about the internal energy and the entropy before the partition function, but all the formulas I know are:
##U=-\frac{\partial \ln Z}{\partial{\beta}} ##

##S=k_B(\ln Z + \beta U) ##
so I guess I need the partition function before, right? Or is there another way to obtain the entropy and the internal energy?
Thank you.
 
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  • #2
To calculate the partition function, you compute the energies of each of the individual spin states, and you compute ## Z=\sum\limits_{i} e^{-E_i/(k_b T)} ## There are 8 possible states.
 
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  • #3
Charles Link said:
To calculate the partition function, you compute the energies of each of the individual spin states, and you compute ## Z=\sum\limits_{i} e^{-E_i/(k_b T)} ## There are 8 possible states.
Thank you!
 
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Related to Statistical physics and magnetization

1. What is statistical physics and how is it related to magnetization?

Statistical physics is a branch of physics that uses statistical methods and concepts to describe the behavior of large systems of particles. It is related to magnetization because magnetization is a physical property that can be described statistically by the collective behavior of many individual magnetic moments in a material.

2. What is the difference between ferromagnetism and paramagnetism?

Ferromagnetism is a type of magnetism in which the magnetic moments of individual atoms align in the same direction, resulting in a strong overall magnetic field. Paramagnetism, on the other hand, occurs when the magnetic moments of individual atoms align randomly, resulting in a weak overall magnetic field.

3. How does temperature affect magnetization?

At high temperatures, thermal energy disrupts the alignment of magnetic moments in a material, leading to a decrease in magnetization. As the temperature decreases, the thermal energy decreases, allowing for more alignment of magnetic moments and an increase in magnetization.

4. Can magnetization be reversed?

Yes, magnetization can be reversed through the application of an external magnetic field. When the external magnetic field is strong enough, it can cause the magnetic moments in a material to align in the opposite direction, resulting in a reversal of magnetization.

5. How is statistical physics used in real-world applications?

Statistical physics is used in a wide range of applications, including the design of magnetic materials for technology and industrial uses. It is also used in the study of phase transitions, such as the transition from a solid to a liquid, and in understanding the behavior of complex systems, such as the weather or the stock market.

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