Statistical Thermodynamics - Help Wanted

In summary, the conversation is about a problem in Statistical Thermodynamics involving three spins placed in an equilateral triangle and subjected to an external magnetic field. The Hamiltonian of the system is described and the task is to sketch possible states and calculate the partition function, as well as determine the magnetic susceptibility of the system at a temperature of 300K. The other data provided includes the values for J and gamma, as well as the volume of the triplet of spins. The person seeking help has attempted to solve the problem but has been unsuccessful and is asking for assistance. The response suggests listing all the energies for computing the partition function explicitly and mentions a trick for rewriting the interaction term to make the problem easier.
  • #1
asynja
16
0
Statistical Thermodynamics - Help Wanted :(

(My translation skills sucks, I hope it is understandable.)

Three spins, placed at vertices of an equilateral triangle, are put in the external magnetic field with density B. Hamiltonian of the system:
[tex] H = -J \sum_{<i,j>} s_{i} s_{j} - \gamma \hbar B \sum_{i=1}^3 s_{i} [/tex]

where first sum runs over pairs of the nearest-neighbour spins and describes interactions between them, and the second sum represents spin interaction with external field; [tex] s_{i} [/tex] can take values between +1/2 and -1/2. Sketch possible states of the system and calculate the partition function! How much is the magnetic susceptibility of this triplet of spins system at T=300K ?
Other data: [tex] J = 0.02 eV \gamma = e_{0}/m [/tex] , where [tex] e_{0} [/tex] and [tex] m [/tex] are electron charge and mass. Volume, taken by this triplet of spins is [tex] 0.1 nm^3 [/tex]

My attempt of the solution was so unsuccessful that isn't worth wasting time writing it in latex. The problem is a form of Ising model; at class we did one problem of finding Z in 1D and much simpler hamiltonian. I thought I kind of understood it then, but it doesn't help me much with this problem.
Help? Thnx in advance.
 
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  • #2


Hi asynja,

I'm not sure what the point of this problem is exactly, but the system is simple enough with only 2^3 = 8 states that you can list all the energies for computing the partition function explicitly. Is this how you're approaching the problem?

There is also a trick for rewriting the interaction term that makes the problem easier.
 

Related to Statistical Thermodynamics - Help Wanted

1. What is Statistical Thermodynamics?

Statistical Thermodynamics is a branch of thermodynamics that studies the behavior of large ensembles of particles (such as atoms or molecules) using statistical methods. It aims to explain the macroscopic behavior of a system by analyzing the microscopic behavior of its individual particles.

2. What are the key principles of Statistical Thermodynamics?

The key principles of Statistical Thermodynamics are the laws of thermodynamics, the concept of entropy, and the statistical description of particles. These principles allow us to understand the relationship between a system's microscopic properties and its macroscopic behavior.

3. How is Statistical Thermodynamics applied in real-world situations?

Statistical Thermodynamics is used to understand and predict the behavior of physical systems such as gases, liquids, and solids. It is also applied in various fields such as chemistry, physics, engineering, and materials science to study the properties and behavior of complex systems.

4. What are the statistical methods used in Statistical Thermodynamics?

The statistical methods used in Statistical Thermodynamics include probability theory, statistical mechanics, and various mathematical techniques. These methods are used to analyze the behavior of large ensembles of particles and predict the macroscopic behavior of a system.

5. What are the practical applications of Statistical Thermodynamics?

Statistical Thermodynamics has many practical applications, including the development of new materials, understanding phase transitions, and designing efficient energy systems. It is also used in the study of biological systems and in the development of advanced technologies such as nanotechnology and quantum computing.

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