Origin of number of bounds in ising model

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SUMMARY

The discussion centers on the calculation of the number of bonds in the Ising model, specifically the formula Nz/2, where N represents the number of atoms and z denotes the number of neighbors per atom. Each bond is shared between two atoms, leading to the total bond count being halved. Additionally, the user seeks to demonstrate the equivalence of the Potts model Hamiltonian to the expression J∑si.sj, where the spin configurations are given as {(1,0), (-1/2, √3/2), (-1/2, √3/2)}. The discussion emphasizes the foundational understanding of these models in statistical mechanics.

PREREQUISITES
  • Understanding of the Ising model and its applications in statistical mechanics.
  • Familiarity with the concept of mean field theory.
  • Knowledge of Hamiltonian mechanics in the context of spin systems.
  • Basic grasp of the Potts model and its relation to the Ising model.
NEXT STEPS
  • Study the derivation of the Ising model bond count and its implications in mean field theory.
  • Explore the Potts model Hamiltonian and its mathematical formulation.
  • Learn about the equivalence proofs in statistical mechanics, particularly for spin systems.
  • Investigate the role of neighbor interactions in lattice models and their impact on phase transitions.
USEFUL FOR

Researchers, physicists, and students in statistical mechanics, particularly those focusing on spin systems and phase transitions in lattice models.

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what is the origin of the number of bound (N z /2 ) in the calculating of average in ensemble in Mean Field for the Ising model?

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Each atom has z neigbours and hence z bonds to its neighbours. But each bond is shared by two atoms, so you have Nz/2 bonds in total.
 
Thanks, I want to show that potts model hamiltonian is equal to this J∑si.sj that siis
{(1,0) , (-1/2 , √3/2) , (-1/2, √3/2)} . how should I do it? what is the first step?
 

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