Troubleshooting the Partition Function for a System with 3 Spins

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Homework Help Overview

The discussion revolves around troubleshooting the partition function for a system with three spins, focusing on the complexities involved in calculating it and the implications of symmetry in the formulation.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to clarify their current progress and seeks guidance on the next steps. Some participants question the inclusion of specific terms based on symmetry considerations, while others mention the Hamiltonian provided as part of the problem context.

Discussion Status

The discussion includes a mix of exploratory questions and clarifications. One participant indicates they have resolved their confusion by simplifying their approach, suggesting that there may be productive insights emerging from the conversation.

Contextual Notes

Participants are navigating the complexities of the partition function, with some expressing uncertainty about specific terms and others reflecting on the implications of their calculations. The original poster's attachment is noted but not described in detail.

annaphys
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Homework Statement
Consider 3 spins s1,s2,s3 on a solid lattice. The spins can have the values -1 or +1. Find the partition function.
Relevant Equations
H = J1*s1*s2 + J2*s2*s3. J1,J2 >0
I'm having problems solving the partition function. I've attached a photo of where I currently am. Am I on the right track? What should be my next step?
 

Attachments

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I'm not an expert in this field but just on symmetry considerations, I would expect there to be a "j_3s_1s_3" term in it.
 
The hamiltonian is given.
 
Solved it. Thought about it too hard. Just need to work out the sums and simplify. One gets then two cosh() functions.
 

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