What Does It Mean for 1D RFIM to Be Frustrated?

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SUMMARY

The 1D Random Field Ising Model (RFIM) is classified as a frustrated system due to the presence of infinite degeneracy in its classical ground state. This frustration arises from the random field, which transforms the system into a spin glass, characterized by random interactions between spins. Consequently, the RFIM exhibits numerous degenerate states, leading to complex behavior that is difficult to resolve.

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  • Understanding of the Ising Model
  • Knowledge of spin glass theory
  • Familiarity with concepts of frustration in statistical mechanics
  • Basic grasp of random fields and their effects on physical systems
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  • Research the properties of spin glasses in statistical mechanics
  • Explore the implications of frustration in the 1D Ising Model
  • Study the mathematical framework of random fields in physics
  • Investigate computational methods for analyzing degenerate states in frustrated systems
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Physicists, researchers in condensed matter physics, and students studying statistical mechanics who are interested in the complexities of frustrated systems and spin glass behavior.

Hermite
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I've read in an article that the 1D Ising Model in a random field is a frustrated system. But what does it mean for the 1D RFIM to be frustrated?

The internet is very unhelpful. I'd appreciate it if someone could answer this for me.

Thanks.
 
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Frustration usually means that there is an infinite degeneracy of the classical ground state. The random field effectively turns the system into that of a spin glass, where the interactions between spins will become effectively random. A spin glass has lots and lots of degenerate states, so I guess this is where the frustration comes in.
 

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